In a world with better economic system, such progress in Artificial Intelligence and automation would have been viewed more positively, I mean who doesnt want to work less and have AI make rapid discoveries in scientific field. Instead we are filled with anxiety and dread of what will happen to our jobs and how we will survive.
I think there should be a political movement that retries socialism with AI. Basically nationalize everything and then automate everything. I think people could get behind that. Basically fully automated luxury communism.
I think there should be a political movement that retries capitalism with AI. Basically liberate everything and then automate everything. I think people could get behind that.
That was a scam or at least overblown in scope, the "control room" you see in pictures was basically a movie prop, and their idea was basically to connect that room to every factory/port/mine with teletypes, it's similar in spirit to what a modern stock should do.
Maybe if they haven't been bombed to death very soon afterwards, control room and everything, for trying to make things better for their population and kicking out foreign neocolonialists, would have gotten an update.
The government does not have an incentive to run anything efficiently as they cannot go bankrupt. Imagine if AI was run like the DMV.
Putting monopoly control of it in the hands of government also makes it extremely likely that whoever is in power will use it to manipulate public opinion + elections as well as encoding their political values into it.
What do you think a Trump-controlled AI would say if I asked about the war in Iran? We’ve already seen examples of companies encoding their beliefs into the system (see Gemini saying nuclear war is preferable to misgendering Caitlyn Jenner), imagine how much worse it would be if politicians were given control instead.
There will always be challenges, as is the case with any system. But I guess I don't really think LLMs will create a bunch of new jobs, so either we look into the future with gloom and doom as we who don't have wealth become part of a permanent underclass as opportunities continue to disappear, or we envision a utopia and work to realize it.
Does the DMV have a reputation for being fast, efficient, or an enjoyable experience?
Personally I remember waiting for hours in a line wrapped around the building for the chance to take my drivers license test.
Another example: have you ever tried to interact with the IRS? The most nightmarish bureaucratic system I’ve ever had the displeasure of interacting with. And guess what my recourse is for them treating me like garbage? Nothing. A company, if they treat me poorly, I can take my business elsewhere. The IRS? The DMV? Not so much.
All of those companies are perfect examples of what I’m talking about.
Chevron: Exxon, ConocoPhillips, BP. From a customer perspective there are tons of competitors which make your life better ranging from QT, AMPM, to Buc-ees (a favorite which people literally LOVE to visit).
Verizon: Starlink, TMobile, ATT, Comcast, etc
Microsoft: Apple, Google, Cloudflare, Amazon (differentiates itself literally on quality of customer service)
The IRS or DMV? No competitor. Unhappy with their service? Go fuck yourself.
The IRS is treating you bureaucratically and poorly because of lobbying from companies and politicians being bribed by said lobbyists.
My point being that you are beholden to a poorly functioning IRS because of capitalism; where companies have lobbied so hard against tax reform and simple filing that it more or less forces you to use their software.
I call the IRS and wait 4 hours on hold waiting to talk to a person. I get disconnected randomly and have to call back the next day only to have to wait another 4 hours. Finally I get in touch with someone and they are extremely rude, unhelpful, and treat me like garbage.
How is this somehow the fault of “capitalism”? Regardless of how the system is structured, the government has a near-infinite budget, they could theoretically staff the agency with enough people to answer my call in a timely manner. They could also train their staff to treat me with human dignity. They don’t do this, and the reason is that they have no incentive to do so. If I am upset by being treated poorly what recourse do I have? Nothing. In fact if I ignore their system long enough, armed goons will show up with guns and arrest me.
There are many examples of government agencies that have this reputation, not only in the USA but the entire world.
“Show me the incentive and I’ll show you the outcome” -Charlie Munger
IRS has been starved of resources following the "starve the beast" playbook.
Also the only reason we have to pay for Turbotax (etc) is due to lobbying. We had IRS Direct File for two years and it was great before being gutted by the current administration.
Your view of the DMV is outdated. There's been work put in around the country to modernize the system. I remember the hour long wait, but online reservations have made my last few visits in recent years take about 15-20 minutes
Prior to Republicans demanding the Post Office fund retirements in advance and various other hamstringing to other services US government was ridiculously efficient
They had to pass legislation to intentionally fuck the books to make them inefficient to fit their preferred narrative because government could be held accountable for inefficiency in ways private corps cannot.
You think people can get behind that? Like if Trump's US suddenly decided everything is state property and Elon Musk will be helping people automate everything, people will be like yeah that sounds good.
There's no such thing. It'd be dictatorial as every other communist state ever was, and that's hoping the people in power wouldn't also subscribe to the communist ideas of killing a bunch of people to enable the revolution and to do it fast. Or read Terrorism and Communism (1920) and get scared - though most people end up thinking these mad men were nice grandpas.
> There's no such thing. It'd be dictatorial as every other communist state ever was, and that's hoping the people in power wouldn't also subscribe to the communist ideas of killing a bunch of people to enable the revolution and to do it fast. Or read Terrorism and Communism (1920) and get scared - though most people end up thinking these mad men were nice grandpas.
Oh come on.
Here's another thing to get scared about: AI and other kinds of advanced automation has the potential to completely undermine the attributes that made capitalism work for the vast majority of people. Rehashing dated mid-century anti-Communist propaganda tropes isn't going to address that. You're gonna need some fresh ideas.
Also people who want to seriously recreate the Soviet Union don't practically exist (outside of some irrelevant weirdos), except in the minds of some really indoctrinated libertarians.
> The sociopaths hijack the centralized assets while exterminating via reallocation all opposition. And the micromanaging from a distance produces catastrophic results.
Am I missing the sarcasm here? The difference from the current system would be...?
It's good that all of these benevolent billionaires are bestowing the world with the fruits of their goodness, and make sure that assets, knowledge and access to the market are fairly distributed. Their political involvement is to the benefit of all of mankind, and does thankfully not lead to the centralization of assets or power in one small group.
Well, so if its all the same- why not just say yes to cooperate-socialism? You just accept that the party (company) owns all the things and redistribute them as they see fit (for the benefit of all) - so wether the bossmann is called stalin or bezos- what difference does it make. Congrats, you got socialism speedrun- you are already at the disilusioned stage where you see the endresult. And thats still a efficient version, because the varous corporate-socialist empires have still to compete against one another. Now get in line critizen.
On what basis do you think that's a good idea? This is a genuine question not a snide comment. I'm interested in your conception as to why it works for you. You're unlikely to respond here but maybe you or someone else will add a helpful link. I will admit that the idea does not 'compute' for me taking into account the nature of human beings - but I'm open to argument.
"Taking into account the nature of human beings" you mean humans' innate desire to help others, to share, to make friends, to spend time working together on shared projects / pursuing shared goals?
Or did you mean "human nature" (I'm using huge air quotes there) as you have experienced it in late 20th century / early 21st century United States?
In the past I've been partial to a society based around self-actualization, like a liberal capitalistic society. However, with the way LLMs are progressing then I think society will turn increasingly technocratic and feudal, with no opportunities for social mobility. I don't really believe that LLMs will create new jobs or opportunities in the long run.
Historically socialism and central planning have been inefficient. With recent technological advancements it may be that the purported inefficiencies are no longer there, and I think a democratic, socialist government will be better at having the interest of the people than private for-profit monopolies. A society where everything is automated and you don't have to work could be pretty nice to live in.
Communism will work the moment communists understand options markets, specifically call options, which is to say that communism is impossible.
Curiously, capitalism will work the moment capitalists understand options markets, but in their case they need to also understand put options, which is to say that capitalism is impossible.
Progress in AI definitely makes the question of economic planification at a state level relevant again, at least for parts of the economy, be it for the disruption it causes to market economy (that was already showing lot of cracks btw) or the capabilities it gives to handle beyond human level complex systems.
In the book Red Plenty, on the Soviet economy of the mid 20th century, there's a section on an abortive attempt at optimizing the command economy using early computers and algorithms to have more effective production and distribution.
The attempt never materializes because some kindly clerk deliberately buries the letter from the enthusiastic engineer, who clearly does not understand that writing Stalin to tell him you figured out a way to build communism better than him, would be suicidal.
It's a fun counterfactual to think about, given that the vast bureaucracy needed for the command economy was one of its major limiting factors. Anyway, interesting book if you are into economic policy or quirky ways that systems can go haywire.
Socialism failed so hard that the overwhelming majority of socialist countries recognized that socialism is inferior to capitalism, bailed, and adopted capitalism. Now that capitalism has brought about AI, socialists unironically suggest reverting to the inferior system, in hopes that it will have (magically) been rendered superior... by a product of capitalism.
This is the self-defeating contradiction at the heart of progressivism: it is a cult of good intentions. It doesn't matter if the promise of socialism has already been proved, on a global scale, to be illusory. It's the intentions that matter, and in their minds no amount of failure will ever tarnish good intentions.
I'm convinced that susceptibility to such pre-enlightenment "thinking" is a Great Filter.
AI isn't making math discoveries. It's generating a metric shitload of syllogism slop, whuch may or may not correspond to reality. We will probably never know, because really who has time for this bullshit?
That's a big part of it, but I don't think it paints the whole picture. We are also losing the bits of work that were actually enjoyable. The challenge, thinking and creativity gave us something we enjoyed. Now we're like border collies in a world with no more sheep and now even the ball comes back by itself.
Another one that comes to mind is Marge Simpson in the Hank Scorpio episode where all labor in the house was automated and she turns to drinking out of boredom.
Scorpio!
He'll sting you with his dreams of power and wealth.
Beware of Scorpio!
His twisted twin obsessions are his plot to rule the world
And his employees' health.
He'll welcome you into his lair
Like the nobleman welcomes his guest
With free dental care and a stock plan that helps you invest!
But beware of his generous pensions
Plus three weeks paid vacation each year
And on Fridays, the lunchroom serves hot dogs and burgers and beer!
He loves German beer!
Or the Grey men in Momo (Michael Ende) who offer time savings through efficient appliances, while stealing the time made free through their use. Their main for is Momo, who encourages her fellow children to play for the sake of playing, which terrifies them.
Is there any evidence that the thinking and creativity that we enjoyed has disappeared?
I'm firmly in the "programming is fun" camp, I enjoy thinking about the problems and solutions, but if I can get a LLM to deal with boilerplate then that's all the better for me.
I'm in the same camp, for the most part. But I also groan when someone checks in 60k+ LOC of vibecoded changes into production, without having any clue how it works. This happened to me recently. I was about start a fun module in the project, but then the other guy just pulled the rug from under me with claude and implemented the whole thing, then moved on. Not sure if I want to work under such conditions.
That's what I thought about 6 months ago: I'm a programmer, not a typist, so I'll just automate the typing part. There are a few problems with that:
1. AI agents aren't just typists. They'll fill in the blanks and implement something that works from extremely vague instructions and probably get it right too, because you and your users are predictable. You could be strict and throw out any changes that weren't explicitly what you asked for, but it becomes tiring and it will shape the way you think anyway. It becomes extremely tempting to increase the boundary of what you consider "boilerplate",
2. You probably have colleagues who don't like programming but please the managers because, of course, everything needs to get done right now, as soon as possible. Maybe one day we'll get organisations where enjoyment and understanding matters, but right now we've got tons of people who got in it for the money, just like to "build stuff" and don't care one iota about understanding (and they're oddly proud of this fact),
3. I'm starting to think the typing was a necessary limitation on output speed. I just don't think anyone can think as fast as LLMs can churn out code. You can easily get addicted to the speed and forgo understanding. Like point 1 this is insidious. If you're not really careful you just won't be able to keep up and before long you too will have a bunch of code you don't understand.
I disagree that what you're describing isn't just another angle of "broken economic system".
The broken economic system is the lack of perceived individual choice, and the priority of business decisions and business profit over individual satisfaction or autonomy.
If we lived in an economic system where maximising individual enjoyment and autonomy was priority, we could give AI to individuals to do with what they want. No sensible human/border collie would choose to give away the fun sheep herding part of their job if there weren't other forces and incentives at work.
But instead, AI is sold to businesses to profit, rather than given to individuals to do the right thing for everyone.
I don't think a system maximizing enjoyment would be any better. Why would anyone choose to work with sewage? Or why would most developers choose to align with rest of the team or with user needs, when programming is most enjoyable?
> I don't think a system maximizing enjoyment would be any better.
That's why I mentioned autonomy too. People like working and being valuable and choosing to add value. The issue is the current economic system doesn't consider things valuable if they don't directly generate a lot of money or profit for a business. An individual developer gets a lot of value from having a job they enjoy where they produce useful code that solves problems. AI removes some of that value for the individual developer whilst promising more profit and value for the business.
> Why would anyone choose to work with sewage? Or why would most developers choose to align with rest of the team or with user needs, when programming is most enjoyable?
Why do people choose to work with sewage now? They're not paid a lot. Programming is most enjoyable when it's useful. Writing code which is going to get thrown out because it doesn't align with your team is not valuable or fun, so why you or any other individual developer choose to do that given the choice?
As a hobbyist developer, I hate busywork. Boilerplate code is the bane of my existence, as is repetitive data entry. Forcing the demon at my command to do it for me so I can problem solve is far more enjoyable, and more efficient in terms of time. AI one-shotting problems is benefited by me thoroughly understanding and solving the problem with pseudocode in the initial prompt. I still do the intellectual work, but the LLM does the busywork.
Also, some things simply are not valuable within a system, regardless of the economic structures at play. Individual happiness is one of those things that has no value under any economic system, specifically because it is a moving target and follows Goodhart’s law.
> No sensible human/border collie would choose to give away the fun sheep herding part of their job if there weren't other forces and incentives at work.
It's not about giving it up, it's about it being taken away. You can't round the sheep up if they never leave the pen.
If something doesn't need doing then it's not work, it's a game. Many people enjoy decorating, but you wouldn't trash a room just to give yourself the excuse to decorate it. A few people might like programming just for the sake of it, but for most it was because we liked doing cool stuff that was hard. It's really important that it was hard.
If things aren't hard then it's just like doing the dishes: it's just time consuming and mildly unpleasant. There's no room for creativity or pride in doing the dishes. Nobody steps back, wipes the sweat from the brow and thinks, wow, that was hard, but I'm really proud of the result. Programming is becoming like doing the dishes.
Kennedy famously said we do things not because they are easy, but because they are hard. We need the challenge. We need it to be hard. If all we're left with is boring work like the dishes, or games, then we'll be like border collies left at home with endless treats and a ball. They can and do get depressed and we will too.
And not just implied: it has been a repeatedly openly made promise, from the start of the industrial age to today, repeated again and again, by scientists, journalists, technologists, futorologists, businessmen, even by sci-fi authors.
By implied I meant "caused". I did not meant "made people speculate that it might do something theoretically". Also, what sci-fi authors and futurologists write is utterly irrelevant here. We should distinguish fantasy and reality.
Practically, technological progress does not implies working less, it implies higher productivity. Which implies more wealth for "someone". Who that someone is depends on political system.
>By implied I meant "caused". I did not meant "made people speculate that it might do something theoretically"
That's on you. Implied doesn't mean "caused".
>Also, what sci-fi authors and futurologists write is utterly irrelevant here. We should distinguish fantasy and reality
A useless distinction, since what sci-fi authors were saying was taken to be a foretelling of things to come, adopted as such by many voices in the wider cultural space.
And of course futurologists were people who made (or attempted to make) informed predictions and even policy suggestions of things to come, not mere "fantasy" peddlers.
>Practically, technological progress does not implies working less, it implies higher productivity
That's your concept of it. Hasn't been historically the concept people (from technologists and journalists to politicians and sociologists) had of it. And even if it matches how things went, it's hardly the only way things could have gone (or should go).
> I mean who doesnt want to work less and have AI make rapid discoveries in scientific field.
A whole lot of people. Anyone who got into mathematics for love of solving problems (which I'm betting is most of them, as it's not like the pay is awesome) will be unhappy if they have the joy of solving problems taken away from them. Your argument here is analogous to saying "who doesn't want to have more children in the world without having to have sex to do it?".
That’s not entirely true. There is joy in being someone who pushed the frontier of knowledge forward, even if only by a hair.
This is evidenced by the scant few people who get into math just so they can rediscover group theory or differential calculus on their own with no spoilers.
So mathematicians are no different from any other labor group that fights automation for their own benefit at the cost of overall welfare. Most artists are unpaid hobbyists, mathematicians should expect the same.
Something tell me that at this point anyone saying stuff like war footing etc, against or for the AI (or anywhere in its immediate vicinity), are just doing it so that they can be one of the few who get benefited from it and are one of the few who also get to be in control and get to have power. Because they can see the writing on the wall and know that one either gets on this bus, or under it. A lot specialist creds/USPs are getting diluted every hour, every day.
This isn't really a political problem. Politics is downstream of what we humans want, and more specifically what humans with power want.
The reason most problems aren't fixed is because you and I rather take our family to Disney Land than feed starving kids. We're don't vote for a political system which taxes us significantly more to try to stop people starving around the world. The problems Tao is worried about already exist for a large part of humanity.
You have two problems here:
1. You're not going to change the human incentive to care far more about their own family and friends and resist the government taking their assets to help the needy they feel no responsibility for.
2. In a world where most people are economically useless people ultimately have no political power. If you're not funding the government or contributing to it's maintenance then government ultimately doesn't need to care about what you want. You could go on strike or tell them you're very unhappy, but so long as the trillion-dollar AI companies are funding them and AI is running the government it makes no difference to them what people think. In fact, from their perspective, all you're doing is consuming resources. AI will likely create a new kind of resource-curse where wealth concentration will cause political corruption.
It's not about what we want, it's about what we believe. All you describe is enabled by beliefs systems, it's above rationalization. What you're describing is just learned helplessness.
On your second point, that rather assumes those 'unless' people will willing to just 'go away'.
That's typically not what happens - you either get bloody revolution or people just ignore the rules that aren't giving them a fair shot ( ie turn to crime - ie state disapproved activities ).
This is what has traditionally held back the elite from their worse excesses - they don't want to live in a world where either of those things happen.
ie what's the point of being rich if you are constantly worried about yourself or a member of your family is going to be violently kidnapped etc.
As to your first point - it's a bit like the first - if there is no social safety net, then it you could happen to you - you could get ill, lose your job etc. Even if you believe the system is created by total self-interest - then the past has shown that the equilibrium involves looking after everyone to some extent as:
1. It could be you one day.
2. Having lots of desperate people, even if it isn't you, is in no-ones self interest.
You seem to believe getting taxed is a choice people make. However, on the one hand economists like Zucman and news stories like the Panama Papers have proven the ultra-wealthy and politicians ("economically useful people") pay way less tax than regular people. And on the other, basically most people disagree with at least some of the uses of taxation, such as a war spending in the US. In fact, sometimes people get taxed without getting any benefits at all in return, such as during government shutdowns.
I think this all calls into question your basic premise that "politics is downstream of what we humans want", ie that the state is an emanation of the collective will of the people, which it serves. The facts fit equally well, if not better, an interpretation in which the state is independent of society and seeks to extract resources from it. This is also consistent with the Weberian state conception in which the state starts as the "stationary bandit" that collects taxes from a village to protect it from other bandits.
Your conception of "economically useless people" is also incoherent. Economic science is about how to distribute rare resources to maximize utility. These people are no less able to work and no less able to benefit from utility and are therefore not "useless" from an economic standpoint. I think you would benefit from just using words like "rich & powerful" and "poor & weak" which if I understand correctly is what you actually mean.
What you're saying in this comment sounds _very much_ like politics, at least modern politics. There's been a few studies that suggest that people's position on the political spectrum is very correlated to their capacity for empathy for others (and in particular, strangers). First example I found on google: https://pmc.ncbi.nlm.nih.gov/articles/PMC10281241/ (note: I do not vouch for scientific rigorousness, I'm saying "some studies suggest that" not "it's proven that").
So:
> you and I rather take our family to Disney Land than feed starving kids
Speaking for myself, it's more true than false (although not that clear-cut). However:
> We don't vote for a political system which taxes us significantly more to try to stop people starving around the world
I sure do vote for that, as do a very significant portion of people. It's absolutely what I want, I am aware of my own biases (and other people's) to prioritise myself, and taxes are a good way to force this redistribution of wealth to happen despite these individual biases. That's kind of the whole point of the left, which is a very strong power in many countries (note: I'm not american and the "american left" is very different from other countries').
So "what humans want" is very much a political question: a very-much-reducted observation of the political spectrum is that it seems that right-leaning people want the best for themselves and their immediate social circle, whereas left-leaning people want the best for everyone.
I don’t think it’s about job security in the case of professional mathematicians. It’s about the fear of giving up the very thing they’re passionate about. It’s not like math researchers work on pure math because of the pay. If anything, they do it despite the pay.
I think you're wrong, and that's bulls*t. Something about virtue signalling.
Not just the pay, but motivation doesn't work on math insight alone. If you look from a distance it's clearly a mix of status, money etc. If what you say was true, many of them would be recluses up in the mountains, but none of them are.
LE. Think about it this way: if someone truly only cares about his ability to do "non-AI-contaminated" mathematics, nothing stops them from ignoring all the AI-related papers and just carrying on on his own. The thing that they are passionate about is not taken away by the field being more rapidly developed. What's being potentially taken away is the impact of their potential contribution.
Why wouldn't you just say bullshit? You didn't even write it in a self-censored format (e.g. bulls**t), you just wrote the actual word with a some funny characters in place of the actual letters.
Some online platform automatically censor or bring about negative repercussions for a given set of banned words. I realize HN is probably not among them, but I still formed this involuntary habit. You have a point tho. It does look much better in what you call self-censored format.
> If what you say was true, many of them would be recluses up in the mountains, but none of them are.
Except, for instance, Wiles and Perelman? And I’m pretty sure that mathematicians are rather more introverted and solitary on average than most people.
In any case, that just doesn’t follow. Mathematicians realize that collaboration is important in math just as it is in most other fields. Humans are also social animals and many of us enjoy collaboration and social interaction for its own sake. And yes, that means social status is a thing that motivates many humans. But nobody decides to study math in order to gain status! Any status stuff is entirely contextual to and conditional on having already decided to study math.
I maintain that you present a picture that's incompatible with how the human nervous system works. And that all humans are driven by the same biological mechanisms, all evolved by pressures to survive and reproduce. Mathematical beauty alone is not part of said pressures.
Humans are built to focus on some objectives and not others at any given time.
Humans naturally prioritize objectives differently. Drives have exclusionary impacts on each other. In both real time and lifetime frames.
Reinforcing experiences further differentiate objective prioritization.
This leads people's behavior to be driven by entirely different net objective directions.
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This diversity would be inevitable due to genetic diversity. But it is also a survival advantage.
Lots of studies show that populations maintain stable diversity of genes for entirely different life strategies, because operating differently from the majority is an advantage.
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We don't actually have a "status drive".
We have drives that tend to generate status seeking behavior but can be subsumed by many different status-like pursuits, such as self-status of solving problems or completing single-person video games, being good at a hobby nobody else cares about, pleasing certain people even to the point of harming any recognizable definition of social status, acting to please (raise status with) internally generated or deceased personalities, a need to be contrarian or difficult to the point of low-social status but high internal status, etc.
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Your assumption that same basic nervous system -> same net drives/behaviors, fails in much simpler species.
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So no, mathematicians are no more motivation clones than they are genetic clones.
And mathematics is not a field that is attractive to people who give social status high priority, because it impedes social status.
It can be a mix of both. There's no reason, after all, that humans no longer being the most intelligent systems on the planet has to mean giving up such a passion, especially since it means living in a world with more and not less mathematics. One has to separate the joy of doing mathematics from a capacity (or, more importantly, need) to obtain a living doing it from the pride of being the best in your field.
It's interesting to recall Turing's own position: "There would be great opposition [to AI] from the intellectuals who were afraid of being put out of a job. It is probable though that the intellectuals would be mistaken about this. There would be plenty to do, i.e. in trying to keep one’s intelligence up to the standard set by the machines, for it seems probable that once the machine thinking method had started, it would not take long to outstrip our feeble powers. There would be no question of the machines dying, and they would be able to converse with each other to sharpen their wits."
On the other hand, Thomas Bernhard's The Loser is a horrifying account of the opposite standpoint---of an essentially second best piano student who cannot stand existing in a world with Glenn Gould.
Major religions, minor religions, cults will have a field day. Or more like a field century or a millennium or twenty, who knows.
Up to a few years ago, I would see or read some science fiction that was medieval times with spaceships (ala Dune) and I would roll my eyes and think “ffs, can’t people move on and invent something more original?”. Now I seriously believe that’s one of the most benign futures waiting for our species[^1]. Not that there aren’t lots of lights in this tunnel, it’s just that its shadows are very black.
Math is more like a treasure hunt than a chess game. Once the treasure is found, it's over. You can try chasing other treasures of course, but now you deal with superhuman competition (which will only become better with time). I can understand this is devastating and depressing
That’s exactly the fear: that math becomes just a meaningless game. Us mere mortals can get enjoyment from solving math puzzles whose solutions are well known, but it’s rather different being in the frontier, discovering entirely novel mathematical structures and proof techniques – and answers to questions nobody knows how to answer yet, sometimes even questions nobody has thought to ask yet!
How can you say that? Even if their future livelihood were 100% guaranteed at the same or even higher level, the loss they feel would be the same. If you don't understand that, you probably just aren't empathetic enough.
Now that all of the trite and boring intellectual work is automated, I can look forward to having it bottle-fed back to me at night. Now get me a gramme in time...
It seems that all AI can do, it can just "replace the average". Write an average quality software, do good enough business analysis, prepare mediocre report, do a bearable, but not so great translation, give you some basic medical advice, which is accurate 80% of time (but what if you are not lucky to have typical conditions?). It can also solve average difficulty level problems in math or physics.
That what it cannot do is to invent new drugs, cannot figure out cheap energy sources, find something better than Standard Model in physics, and anything that would contribute to overall human progress.
The result is that it can replace a lot of jobs, it will efficiently killed any research done and the level of master/PhDs, because majority of those can be done now with the help of AI (we already see this, the burst in new scientific articles - nothing groundbreaking, but publishable).
As a results we will have soon a gap, as only very determined people would go into science, analytical jobs, etc.
In one way, this is OK, we had too much science research that was done only for the sake of producing more "papers", we also had a lot of people in the companies doing "bullshit jobs".
But on the other hand, we might face soon situation in which there will be almost no people in Academia, so who will teach people, in addition, science worked often by doing wrong, unreasonable, crazy things, testing vague ideas and come up with something new and great. This required a lot of people doing science without any good results coming out, a lot of seemingly wasted effort just to hit several great ideas (a bit like Venture Capitals work).
This might also lead to decreasing number of white collar jobs. We can have a new "rust belt", the one for blue collar fall happened because of jobs offshoring, now we are "offshoring" white collar jobs to a few companies who offer AI models.
This all will affect badly society without any huge, visible benefits for it as a whole.
I am not a mathematician, but from what I understand, mathematicians just do not not see this as progress. They see it as being robbed of potential progress. Mathematical progress is not achieved in the solutions to hard problems, it is achieved in the method of finding the solution. We are being robbed of the opportunity to find the solution by being handed the solutions.
I am also not a mathematician, but I think this is an assumption that people are making. It could be that by reading the solutions/proofs of these AI-generated results, those methods could still be discovered, ie. the AI could be discovering new novel methods implicitly. It's not exactly the same thing, but when the Navier Stokes blow-up "solution" came out, there was a lot of hoopla around it being stolen and not novel, but then once the dust settled, we had this:
> But closer examination reveals that OpenAI’s proof builds its unnatural force in a totally distinct way. The proof’s similarities to Buckmaster and Alpöge’s progress are superficial...
So I think more time needs to pass before a call can be made.
An interesting thought experiment is this: if we were to go back in time 150 years and tell our ancestors that Newton is just an approximation and give them a 5,000 page book about Special and General Relativity, QM and QFT, would we be robbing them? Initially the whole thing would be incomprehensible, but eventually they would chew through it and make sense of it. I don't really know the answer (and perhaps the analogy is not great since we're quite attached to our physics heroes from the last 150 years).
there is a difference between "knowing" and "knowing about". "knowing" is having it deeply ingrained into one's intuition by working at a solution over years, often without progress in the immediate sense, and often without success in the absolute sense either.
Other than the person who developed the solution, everyone else will have to be "knowing about" it by studying written texts and lectures produced by someone else's mind.
That is the case many fields. Mathematicians, like physicists, are trained to develop a strong focus on methodology and intuition. It seems likely that the dynamic by which that intuition is gained will change.
> We are being robbed of the opportunity to find the solution by being handed the solutions.
I find this argument difficult to understand. As a math student in college with no ambitions (or realistic opportunity or aptitude) to pursue original contributions to the field, everything I learned was by definition already solved. Nevertheless I was able to - required to, in fact - work through each solution in order to develop understanding. And I did in fact learn by this method, as countless other students did before and after me.
So when I hear this argument from mathematicians, all I can hear is that they are frustrated at being out back into the position of being students, where the end result of the hard work of understanding is just the understanding itself without the prize of a new discovery. If they want to find the solution without reading it, they are still very much able to do so, just as their students do every day.
Difficult problem -> Developing new branches of mathematics to solve said problem -> solving problem, or failing to do so, it doesn't matter -> aforementioned new branches of mathematics are used to solve practical, real-world problems that benefit industry and economy.
The point of solving the problem is not the prize. The point of solving the problem is not even solving the problem. It is developing new methods and deepening understanding to drive useful applications.
> It is developing new methods and deepening understanding to drive useful applications.
Knowing that a solution exists is not an impediment to deepening your understanding of a problem.
For example: Knowing that there is a proof of Pythagoras’ theorem is not an impediment to thousands (millions?) of geometry students developing the intuition that comes from drawing the famous diagram where the number of squares visually add up to one another.
What about the existence of an AI-generated proof prevents a mathematician from working through the problem on their own to deepen their understanding, as if the proof didn’t exist in the first place?
I'm baffled that you find the mechanics of human motivation hard to understand, (presumably ;) being a human yourself.
Studies have shown that people that know a certain piece of knowledge is stored somewhere, are less likely to remember said knowledge.
The sense (thrill?) of exploration and discovery can in fact be part of a person's motivation. The popularity of open-world games (often derided as 'walking simulators') are a testament to that. Do you really not see how that could be undermined by knowing that a problem that interests you is already solved?
there is a lot of thrill of exploration and discovery with things you already know to be true.
Basically all natural sciences work that way. Knowing the truth of an apple falling down a table when rolled over the edge is the beginning of discovery, not the end of it.
Mathematical discovery also worked more like theoretical physics 200 years ago. The modern way of formalization in maths might be dead now in some ways, but it's also only 100 years old.
There's still many ways to do modern maths and have a lot of fun with it that are not taken away by AI.
Because they've been through this process as part of learning math. e.g. you read your analysis book, and come to:
> If a set E in R^k has one of the following three properties, then it has the other two:
(a) E is closed and bounded.
(b) E is compact.
(c) Every infinite subset of E has a limit point in E.
You stop reading, and you figure out the proof. Once you're satisfied, you continue reading the book and compare with its proof. The people who managed to get far enough that they were doing research have almost certainly gone through this exact process. They've self-selected as individuals who are able to motivate themselves to learn things even when they're already known, and to be able to figure things out without being given the solution. There's an insane amount of math to get through to get anywhere near the frontier, and it all builds on itself such that you can't just skim and skip, so they must have already learned to be able to do this.
Likewise, when given an exercise of the form "Prove P" or even "Prove or disprove P," you can be pretty certain 1. it is doable and 2. it is doable using techniques/theorems discussed in the course/book you're working through. But people are perfectly happy to do this for several years.
When you're learning/internalizing existing knowledge, you tread a defined path skipping unnecessary stops and diversion and heading instead directly to the destination. The destination, not the journey, is the point.
When you're discovering new knowledge in the form of proving/disproving, there's no defined path to follow, so there can be quite a bit of backtracking and diversions and detours into other areas you weren't planning on going initially and while there might be some well-defined paths to follow, you might have to cut your own path through uncharted desert or jungle.
All those diversions and detours make the journey just as if not more important than the destination because they create new destinations of their own for future travel that would not have been spotted or noticed for a while longer (if ever) otherwise.
So to bring it back to math, transitioning from having to develop proofs for theorems to validating/learning extant proofs completely changes the scope of future discovery. Everyone will tread the exact same path to a proof/theorem and then stand in the same place to look for future destinations and then use AI to build them a path to that new destination and then everyone will follow the same path to the new destination and repeat the process, so the chances of finding something curious along the way plummets. And something curious could be an entirely new field of math, or maybe just a new problem that isn't relevant to the intended destination but gives a view of many new never before seen destinations for future trips.
I think it's bigger than that. There's an unsaid anxiety around this that I don't think people are properly quantifying yet but is probably bubbling around inside their subconscious: we may soon get to a point where computers and machine intelligence outstrips our own and is able to solve mathematical and logical problems that are not just unsolved because they are hard but because we are hitting an inherent limit in the concepts and problems our physical brains can comprehend.
Demis Hassabis has talked about this a bit in regards to theoretical physics and it's an idea that I think I agree on. Every once in awhile we randomly get a super genius who's brain is seemingly able to conceptualise or visualise beyond the state of the art. But at some point I think we have to accept that we are just animals and inherently limited by our brains (and means of observing the physical world).
The scary part isn't that AI is solving the unsolved problems that will force people to act like students again. The scary part is that we may not be able to understand the work needed to get to the solution at all.
Obviously we're not quite to that level yet but it's entirely possible we do get there. And on the optimistic side ~ maybe that's what we need: better tools.
This reads to me like Victorian fears of buildings over three stories (you'll asphyxiate) or the idea that humans will die instantly when moving faster than a horse could carry you.
I see no reason whatsoever to expect that humans have any kind of limit to what we can understand as a species. We've had more unthinkable and incomprehensible discoveries than anyone cares to count. They become understood, normalized, and folded into our scientific canon. We went from inventing airplanes to landing on the moon in a matter of decades. We went from banging rocks together to quantum physics and string theory. I think we'll be alright.
Hypothetically, if a solution to a problem requires a billion intricate steps there is no way for humans to comprehend it. Human life span is too short. We can't even grasp what it entails. If a machine can pump out humongous proofs and solutions on a regular basis we will never catch up.
I'll add to it. The classic answer to your objection is "but as a species we'd have sooner or latter 1 billion steps worth of intellectual capital". Today someone gets to an intermediate result worth 1 million steps, tomorrow another million and so on.
But there's no guarantee that such "low IQ" intermediate steps exist. We do well with many classes of problems because of divide-and-conquer. But not all problems can be solved through divide-and-conquer.
For a rough analogy, see how AI plays chess and intermediate board positions often don't make sense to us. Imagine now an enormous chess-like game played in an enormous chess board where a match lasts longer than a lifetime and none of the intermediate steps make sense to any human.
I know what they are saying but it's really difficult for me to separate their job-preserving and peer-acceptence instincts from their opinion. I don't see how it couldn't be biased.
I remember a recent "100 hundred mathematicians on AI" post recently. Some of them appeared truly excited even if the majority wasn't. Who's right? Who's biased? I don't know.
I don't. Start with automating the jobs people hate, assholes.
Right now you're doing the equivalent of telling athletes that you've solved sports, and they need to sit back and stop playing so that we can enjoy progress in goal scoring.
Yes, we have to cope with the torrent of shit that's being pushed at us by misanthropic douchebags. It would be nice if they weren't degrading quality of life, but we just have to cope.
Nobody is misanthropic. Technology comes as it naturally does, new discoveries are more of a natural process than something any person can control. It just so happened that we got the automobile, it doesn't matter who was prepared for it or not, just the same with AI.
It's a little funny how quickly the conversation goes from "AI will never be able to {my-field}" before turning into "We cannot have AI ruining {my-field} with its obviously superior abilities"
If OpenAI had never made a push to get good at maths, we might still have a sizeable group of peopne stuck at that first line. I say that because I still hear in discussions the naive rebuttal "But we'll still need _someone_ to {one-step-up-in-hierarchy}" . Although you have to be curious now how long that sentiment can last.
The good news for those doing abstract maths might be that, now that OpenAI have proven that their AI can do the job in principle, there's probably not much left in it for them to keep going. Mathematicians should know better than anyone the lack of a direct profit motive in doing the work that they do.
I guess you didn't read the article? The end of it quotes Tao about how much more there is to discover in mathematics, and he expects humans using AI to get there.
My point was not that AI from now on should be done away with in mathematics research. I was rather commenting on the likelihood of AI companies continuing the "strip mining", as Tao put it, of his field.
Hacker news is not really a good place to talk about nuances involving academia. I don't expect VC minded hackers comprehend how someone can devote years of their lives working minimum wage trying to answer questions which earn them a fancy title on a piece of paper, for that matter.
A lot of us here are VC minded hackers *because* we spent years of our lives working minimum wage jobs in academia and then eventually realized we preferred to build!
> A lot of us here are VC minded hackers because we spent years of our lives working minimum wage jobs in academia and then eventually realized we preferred to build!
This is a disingenuous framing. I've "built" more in academia than in some jobs I had, and some VC-backed startups are renowned not for building but for their lack of ethics.
Reward alignment is the differentiator. Obviously it's very far from clear-cut what is worth funding in research. But i've seen a lot of crap research, that would have died off far sooner if it had some VC/free market equivelant.
Or preferred to eat. I love teaching, and I'm good at it. If it were more valued by society then I'd do more of it. As it stands, I'm in adtech, and I teach a little piano and math on the weekends.
A large fraction of people are open source contributors, hobby game devs, and various other types of people who fall under "devote years of your life with no formal remuneration"
The US-American mind cannot comprehend "free time" nor working hard on something just for the love of it and the joy of collaborating with other like minded people.
There's a reason that so many open source builders and contributors are unemployed people in social-welfare European states. There's a reason that nearly every great work in the English canon was written by someone who was on the dole at the time, from Nietzsche to Harry Potter.
> If OpenAI had never made a push to get good at maths
By snooping on work math researchers were doing on their platform and then overtaking them when sufficiently close to completion? isn't that what happened i'm not sure
No, as far as I know there's no evidence they used the other team's work for their own (and OpenAI changed their initial 'It's possible' to 'we double checked and it didn't happen'). What they did was hear a rumour about it and then spent millions of dollars on compute to scoop them.
That's not what happened. The claims of this for Navier-Stokes were already exagerated. It was dramatic but there was AI involved on both sides to make progress and the final proof did not use the same approach.
Finally, the list of hundreds of solved problems after that completely defeated any argument in that direction.
so far it's been programming and math, the two fields most people would naturally assume computers would be good at :P
not saying it's not possible ai will continue to expand to more fields, but i don't think it's a coincidence that both math and programming are easily automatically verifiable. in fact for programming their effectiveness drops substantially once you remove any sort of testing or verification loop, and i imagine it doubly-so with math. try getting an agent to build something without any tests or verification, you'll see it go back to near-2024 levels. half of the work i do with agents is setting up a harness that can take and analyse screenshots, send direct input to the application, and compare results. this is something that should come standard with every harness.
if we can build automatic verification for more fields is a different and perhaps more relevant question.
> so far it's been programming and math, the two fields most people would naturally assume computers would be good at :P
If that is true, then only because "most people" have no understanding of what differentiates programming and math from "computation". Computers (as the term suggests) have always been extremely good at the latter, and useless at the former. It's only 2–3 years ago that computers, by way of LLMs, have started being good at the former.
I have to confess to being wrong in exactly that way in the past. On the other hand it is probably always good to behave as if the next step up in the hierarchy is still available. There's no point letting these things spoil your day twice.
Now I'm forced to think about it much more carefully. I don't believe that current LLMs can find every possible proof on their own from now on. I also agree that the PR returns have fully diminished. Given how hard it's been in recent years to fund e.g. a poorly paid postdoc, I doubt there's a ton of money lying around for getting the best models to work on mathematics problems. I think there's a chance we're heading into a really good era. I was able to make so much progress back when Google search was a useful research tool...
I'm of two minds about this. On the one hand, you get miraculous results with AI, and that is what you are referring to with "be able to {my-field}". On the other hand you regularly get useless, if not toxic, crap out of the miracle machine. If you work with AI, you know these moments: "no that is not what I meant at all!" [1] or "how could you have already forgotten the central motivation I laid out just ten back-and-forths ago?". We're calling this the jagged frontier, but the jaggedness itself is not the problem, it's how deep these cuts go into aspects that are important. These are, why AI is still not "obviously superior" in its abilities, can't replace mathematicians and software developers and lawyers and everyone else who is primarily working with text. (It's also why people say it is ruining their fields, instead of replacing them in their fields, because it only replaces some part of the work, and what's left is not tenable or pleasant (e.g. doing reviews all the time).)
Over all, I'm not quite sure whether I see these deep cuts occurring less and less with progressing AI. It might just be, that I'm giving them progressively harder tasks as well. But the fact of the matter still is that they aren't there yet and it needs proof they will get there ("there" being able to do competent work that is not strongly limited in their scale by human review and correction). So I'm still not convinced about the point you want to make, even though I see AI disrupting about every part of society, and am hoping for the benevolent super AI to lead us to utopia (and afraid of the cliff of human dictatorship on one side and extinction on the other).
[1] I've started to use these moment to reflect on whether a human in a comparable situation would fare better. Having only a few text inputs and small glimpses into a code base and knowing next to nothing about you or your project personally. Quite a few times I've concluded: No, they would not. But more than 50% they would, and also, these limitations are technological limitations of LLM, so you should probably not excuse them for that.
But isn't part of the problem that you simply don't have access to the hardware larger organisations do? OpenAI certainly run into the same constraints. but if they have access to terabytes of memory, while when you use the same model it's closer to 32GB, that will surely affect how the model behaves?
So the pain points you and I frequently run into, simply don't exist for a well connected individual(Sam Altman).
Has OpenAI shared any new interesting _problems_? I.e. do more than strip-mine mathematics, as said in the article, but said: "Here is a question I cannot answer, it's interesting for this and that reason, I believe it's true for this and that reason, it's beyond me though, have at it." Has that happened yet?
Considering that this is where the mathematician excels over machine wouldn’t that only offer a new view from such a mathematician that “OpenAI has rapaciously stolen from mathematics that last dignity: of choosing worthy problems”? Perhaps with sufficient effort the community of mathematicians may yet forestall such an effort.
I'm in this boat too and I find it a bit strange that this hasn't been more emphasized by mathematicians themselves.
So far, a lot of the hullabaloo has been around solving legacy problems, but more interesting and more important for actually progressing mathematics is the generation of new insight and new problems. Someone had to pose all those problems OAI is solving in the first place, in some cases, ages ago.
The collective letter response to navier strokes, sort of touched on this, but still didn't really emphasize the epistemic value of problem generation explicitly. I find it sort of strange that this has been so underemphasized.
I think their expectation is that “problems” as we’ve understood them just won’t be nearly as important to mathematical research going forwards. The field will look more like e.g. economics, where progress sounds more like “developed our understanding of the microeconomic foundations of macro” than “breakthrough on the Coase transaction cost problem in five dimensions”.
I've never heard a particular reason why the Millennium Problems were of special interest. They had resisted solution despite significant effort, but I don't know if Riemann or Navier and Stokes had ever singled those out as especially high priorities. They started as ordinary problems and became known for their durability.
So I'm not sure if it's something we should expect from a machine, just because we don't expect it from mathematics either. Maybe the machines will interrupt that process because we've changed how we go about looking, but perhaps not because old problems are solved.
In order to celebrate mathematics in the new millennium, The Clay Mathematics Institute of Cambridge, Massachusetts (CMI) established seven Prize Problems. The Prizes were conceived to record some of the most difficult problems with which mathematicians were grappling at the turn of the second millennium; to elevate in the consciousness of the general public the fact that in mathematics, the frontier is still open and abounds in important unsolved problems; to emphasize the importance of working towards a solution of the deepest, most difficult problems; and to recognize achievement in mathematics of historical magnitude.
It then goes into details in each of the chosen problems.
If your takeaway from all of this is that some other group of people has the special-est skill that can never be replicated by a computer, I fear you’re missing the point.
How does that make any sense? Why do you assume that someone more intelligent would not be able to wield any AI tooling better than an average or below average human? Just curious if you're thinking short term or long term on this.
I mean, clearly "tooling" is not a perfect analogy for AI. As others have pointed out, if you pay money and get back a full website, app, game etc. it feels a lot closer to a service.
It's like asking why an expert pizza maker is not in a better position to succeed now that he has an excellent pizza delivery number he can call to have one available to his specification in an instant.
This tool belongs to somebody (capitalist!) else and in a new world better tools will always win, not individuals anymore. And it feels like to go from being Rembrandt to CVS employee who takes passport pictures - result much better quality and cheaper but no skill and glory.
Interestingly, the dynamics strongly resembles the industrial revolution when from highly skilled manufactures society moved to factories with power machines. And it all came down who owns means of production. Now AI is a new means of production for all white collars jobs and if the industrial revolution taught is the way to go, nothing good will come out of it.
That’s like thinking that computers will belong to “capitalists.” It’s already clear that AI is going to be a commodity you’ll be able to rent for barely more than the price of electricity.
I'm somewhere in the middle on that. People used to think that computers would be owned only by large corporations, then home computers appeared and improved. It's getting tight now that logic scaling is mostly exhausted, at least with current operating principles. Even so, new specialized hardware and model improvements may help (for inference). Training seems to be the biggest problem, it seems hard to democratize.
Nothing good for skilled labor you mean, especially in the short to medium term - just like in the industrial revolution. If the new technology is any good, it will produce desired things (let's say medical breakthroughs?) faster.
I don't particularly like AI, but if AI replaces developers and other knowledge workers, not everyone is worse off, and I don't mean just capital owners.
No, but someone who has trained their whole life to run fast, surely will be able to coach someone else to run faster than someone who has been on the couch watching television?
I use LLMs to great advantage, solving problems in my domain. I no longer make for loops.
my point was that the new future where running faster doesn't matter any more might come, because everyone is driving (and potentially can't run much at all).
but the analogy would be a riflemen trained to aim, and a person pressing button for guided missiles. How good you are at the original task is unlikely to matter when the new way supersedes the old way.
Over someone who never fired any real weapon? Probably. You are not startled by violent sounds. You have intuition for ballistics, time to target, CEP, weather effects.
The social fabric that produces math got ripped up by marketing guys who didn't even bother to check their work.
He described it at 'strip mining', 'rude', and said that many grad students, who are given problems like these as a part of their training, had the rug pulled out from under them (because its customary to let people know you are working on something to prevent this kind of thing).
And your whole analysis is that Tao is worried about his 'identity', status, and 'being a differentiator'.
This is projection on your part. People have values that bear no resemblance to yours and it would behoove you to learn to recognize that.
Well they've been doing that to devs for a couple of years now and yet mathematicians seem to be much more vocal whingers (might be selection bias in the articles I'm reading though).
AI is coming for all of us knowledge workers, nobody is immune.
The rug being pulled is the expectation of a reasonably high-trust ethical environment. The question to be asked is: What will graduate study look like in an utterly zero trust ethical environment?
If there is still such a thing as graduate study. If there is still such a thing as study. Tell me what to say to someone about to enter college about why it isn't a waste of their time.
Most colleges, even before LLMs, were already a waste of time for most students. I mean they were somewhat effective for networking and economic signaling to employers but they had already lost the plot in terms of real value to society. And now with LLMs the entire education system will need to be rebuilt. Let's get to work.
This was already why people went to grad school. I think people weigh a complex bag of known and perceived motivations and risks. One of the risks is that your project gets "scooped." There were some weak ethical and practical safeguards around that. But completely rearranging the risk equation will change peoples minds about whether graduate study is worth it.
Disclosure: PhD, early 1990s. In my case, replicating my project would have required a sizable investment in equipment, much of it was purpose-built, among other things.
Interestingly we're a few months away from a data point on what happens to grad school applications.
It doesn’t exist for OpenAI’s benefit either. The point of the “strip mining” analogy is that they are churning through the mathematical landscape in a way that optimizes for the number of problems solved rather than the amount of understanding of those problems.
But is understanding the end goal? Understanding for the sake of understanding? Or understanding for the sake of being able to solve problems for the benefit of humanity?
Yes, understanding is the end goal. That’s what defines the field of (theoretical) mathematics. There’s a separate field, called “applied and computational mathematics” or just “applied mathematics”, for research that focuses on computing concrete results.
Strip mining interesting conjectures. AI can answer interesting(pedagogically valuable, carrying important implications, etc.) mathematical questions in formally correct gibberish far faster than mathematicians can generate them. Until AI can replace the conjectures it resolves on its own, it's consuming a finite resource.
No. Genetic diversity and natural selection have created many intricate, beautiful, and useful structures. Unless someone is willing to argue that Darwinian selection is sentient, it's clear that theres at least one non sentient process that is creative.
The papers created by AI on math, right now, are torturous reads. Figuring out what is actually going on in them, is the work of months or even years.
I’ve seen multiple conference submissions that read like English, but take hours of effort to disentangle and figure out what they mean.
There is a limited number of known interesting problems that are worthwhile to engage in. New ones are found and understood, but it is a slow process and it is dependent on understanding and verification, not generation of content.
Saying AI will create new ones, strengthens the strip mining analogy. The idea that AI will find other problems parallels the idea that firms can cut down a forest and plant them elsewhere.
The conversation on HN is driven by non mathematicians, to whom math is a subject, like “nature”. It’s not their core business. The original post by Tao is a better source of information on what he means.
It can't consistently produce new, interesting-to-humans conjectures faster than it solves open problems, no. AI-generated natural-language proofs are more or less human-unreadable and are solely concerned with the process of constructing whatever object serves as the counterexample. Natural-language counterparts of formally verified proofs are often unfaithful to the formal component. All of this combines to create less-than-fertile ground for future study.
It is usually not the monopolist who is protesting against strip mining, it is usually the monopolist doing the strip mining and the environmentalist protesting it. Which is to say, I don’t think mathematicians are claiming a monopoly on mathematics, but I think AI might.
It's time for the social fabric of math to be ripped up, it's an industry being disrupted.
No one has the right to prevent others from working on a math problem. If you're working on a problem the best way to not get scooped is transparency: publish whatever you have as soon as possible.
Tao's behavior is most consistent with any other worker resisting automation for selfish reasons.
Tao is very prominently an early AI adopter. He, and other mathematicians, have fruitfully integrated it into their work. The way it is integrated matters, and it is carelessness and selfishness on the part of OpenAI that he is objecting to.
> It's time for the social fabric [of math] to be ripped up
This is the attitude of a social arsonist. You can, and should, integrate changes without maximizing destruction for its (or Altman's) own sake.
> an industry being disrupted.
This is the SV euphemism for law-breaking and monopolist practices in a country that has forgotten how to prosecute those with the most power and privilege.
> This is the SV euphemism for law-breaking and monopolist practices
Quite the opposite. The mathematicians are the monopolists who are upset that new-comers are able to do their job better than them, and even worse, they are giving it away to the world for free!
The horror! People giving knowledge to the world for anyone to use freely! Won't someone think of the oligopoly that was coordinating to make sure each of the gatekeepers get their slice of the pie?
Monopoly: Exclusive control of a particular market that is marked by the power to control prices and exclude competition.
Mathematics is collaboratively and publicly produced, it is vetted for free by peers, and results are publicly available. There is no 'market' and no 'price'.
These results, like the invention of LLMs, are often used by private companies for the generation of private profit.
"Open" AI used a private, unreleased, for-profit model to generate those papers.
What, precisely, did the mathematics 'oligopoly' gatekeep you, or anyone, from?
> their slice of the pie
There's very little money in academia, and even then, its a struggle to get any funding at all. What are you even talking about?
Final point, 'knowledge' is socially produced as well. Until the papers are accepted, they are machine artifacts that might be knowledge, but that same system you disdain will be what incorporates and validates those insights.
Until AI agents are embedded in glasses and everyone gets comfortable with sending their conversations to AI, the smartest person in the room is still going to be the smartest person in the room because they say smart shit. Or until the dumb guy types into their phone and says smart shit. Given the pushback to Meta's glasses, I think that'll be a differentiator for a bit longer still. Even before LLMs, you could check Wikipedia and different rooms treat the people that do that in different ways. And then there's the "Don't be a meat proxy" movement.
Not all rooms are real face to face. Smartest person also needs time to think and lookup information. Worst smartest person can think on one hypothesis at a time.
What? This is like a drive by shooting or something. Several PhD students almost certainly lost months of work, and others considering a PhD will have more doubts. Those problems aren't necessarily important because of the solutions, but because mathematicians can make unique contributions to mathematics in the process of solving them. LLM proofs haven't created any new mathematics techniques.
Everyone who built an identity on earning a living doing useful work for other people is going to have to come to grips with that no longer being part of their identity.
No. It's just people who built an identity on the power that their intelligence afforded them. We view that power and the intelligence itself as the same thing, but they're actually separate.
I don’t think that is correct. For consistently good results, you need to set the right goals and be able to judge the quality of your outcomes. Even if you don’t do the hard work in between some thinking is required for non trivial work.
You're out of date. The chats that found new Riemann conjectures were "look for a solution to the Riemann conjecture", followed by a bunch of "you can do it" and "I believe in you". The same goes for other breakthroughs, where the people involved didn't even know the math.
Yeah that's an interesting point of view. In my studies I got comfortable with the fact that there's always someone smarter than me.
At the same time it should be considered that with physical labor workforces lost their income source numerous times. Ironically they are currently being considered a safe haven.
I just finished reading "Outsmarted: The Hidden Costs of Being the Smartest Person in the Room".
Most of the HN crowd would resonate a lot with the points raised in this book.
The last(-ish) chapter does have a section on how AI has robbed the "cognitive elite" of our identity.
Elite pure mathematicians are like elite rock climbers or mountaineers. They desire the satisfaction of sieging the face or mountain and attaining first ascent[1], especially on faces that weren't considered humanly possible. It is an art form and there is much satisfaction and discovery in the process.
OpenAI is Doctor Octopus who just buzzed the climbers. They've proved there is a route, but so far can't explain it in a way that is intelligible leaving the climbers to catch up. Or is the AI making leaps of logic too complex or out of reach for the climbers a la the four-color-theorem[2]?
I find it weird to blame OpenAI for using math as a benchmark. If they hadn't done so, then in three months, say, after releasing Bel, someone else would have used math as a benchmark for it (like mathematicians already do since Fable 5 and 5.6 Sol). The result would have been the same (hundreds of open problems solved quickly).
It isn’t a benchmark though. Not yet. They rely on mathematicians to check the proofs including all lemmas. And on other mathematicians checking the reviews. Without being on the OpenAI payroll of course. Now they have flooded the zone, overwhelming the review capacity of the whole field by at least one order of magnitude. It is the move of 15-year-olds holding tools they shouldn’t have access to.
Did they force anyone to focus on reviewing those results instead of other ones? People choose to focus on them for a reason.
I think it's always better to publish preliminary results early (as long as you clearly say so, and they did), and let mathematicians decide which of those are worth focusing on.
A few people spend all their focus and tokens on one problem, and after some time I expect one of them to get at least closer to a solution. They can either work independently, or even better they team up and create a shared scratchpad for their agents. I don't see limits to scaling this, compared to OpenAI running however many subagents per problem.
And that multiply those few people by number of different problems.
No, that's not what I say. My argument is that once the Torment Nexus is built, it is stupid to argue that they used it to torment people, when someone else would have tormented people with it anyway. If one wants to argue something, it's that the Nexus should not have been built.
And I honestly have no idea what Tao wanted to happen. How could you ensure that the AI "empowers" scientists and doesn't replace them. Intelligence is intelligence. If it's powerful enough, it will replace other intelligence.
I very much wish they'd just let mathematicians have at it empowered by the model so we could all treat the people who claim they have a lean verified proof with an unintelligible explanation as the crackpots they are.
IIRC, Ramanujan[1] was given a book of Math results as a child and independently proved each result in a way that was original and often unusual and opened the field to a lot of discoveries. The Math establishment had a hard time wrapping its head around his proofs, like an alien genius, like an AI.
I feel that there are some surprising blindspots within this thread, in sympathy to mathematicians.
Don't we as tech ppl understand "purpose"? You might not feel purpose in their work, but surely you see how when it comes for your own, you might revisit why it is such an imperative that we give AI all tasks for want of speed and efficiency?
“Much as one cannot unhear a movie spoiler or a crossword clue, one cannot explore a problem as profitably and richly once one is aware of an existing solution.” He mourned, he added, “the path not taken, and the opportunities lost in the frantic race to develop this technology.”
This observation is so important. There is unintendedly something being taken away from us that cannot be given back. And it's a pure loss, there is nothing returned to us on an experiental level. It already existed before that "somebody else" would solve or discover something. Now this "somebody" is just just an alien nobody can relate to. And that "something" is everything.
Even if AI solves ageing, and climate change and whatever else; as humans we'll have lost something beautiful and precious. There will just be less of this sense of wonder and curiosity.
Sounds like the earlier feeling of trying to do software development in the age of having executives trying to move most of that effort offshore to "arbitrage the labor differential".
My gut tells me that we would be fine with that. LLMs are viewed differently by many people, and I can't decide whether people are so naturally opposed to these discoveries because the LLMs were manufactured by us (and should therefore be in someway inferior), or because the LLMs lack a 'soul'. It's a very interesting question to ponder.
My thoughts exactly. As far as I am concerned, super-intelligence that dominates pretty much everyone in mathematics already existed. Yet I didn't hear anyone declare that the existence of Jean Bourgain was a tragedy for mathematics. Why is it different when it's a machine or, as you mention, extraterrestrial life?
No, but the solutions they gave us would be pretty useless unless paired with understanding.
The societal rewards of the mathematical community's pursuit of answers to problems is not primarily in the answers themselves. It is in the practical problems that are eventually solved not by knowing the solution to the initial problem but by means of the new branches of mathematics that were invented to solve it.
Are you really unfamiliar with the concept that "the journey is the destination"? Read a book.
One aspect that currently frustrates me is that even paying for the highest plans and spending multiple quotas across all flagship models, I still haven’t been able to reproduce any of the amazing feats Anthropic and OpenAI gush about.
I suspect their internal harness, models, and thinking budget far outstrip anything us peasants have access to (never mind the compute).
So saying that they achieve all these headline results with 3 hours of GPT Pro is disingenuous. If that were so, hundreds of math phd students would’ve already recognized it.
I’m coming to the realization that my monthly subscription is only helping subsidize their real internal AGI, and my interactions are a small amount of human feedback and creativity which they can strip mine should they choose to.
They have been nerfing the models for us plebs for a while now. Anthropic does the same, and if the Chinese models aren't doing this already, they will eventually.
It's hard to prove, but I'm personally extremely convinced of this. The point of AI (from the perspective of these companies) is to solidify and centralize their control of the economy and the world.
If you ask Qwen3.8 to give you a list of things it would refuse to help you do, it will list a number of things related to building/creating/training/altering LLMs. This didn't make much sense to me until I read that the #1 thing these frontier companies are optimizing their models for is training/creating/editing newer AI models. That makes a lot of sense to me now, and that's also something which they will want to keep 100% under wraps.
Therefore the #1 focus of their research and efforts and expenditure will be something that they don't want any of us to get access to. I think many other behaviors like model nerfing follow from that. It helps explain these frontier research products which we ourselves cannot get access to.
> Of course you get a lot of right-wing people saying "oh these Poles; they come over here taking our jobs". I think if a guy from Poland arrives and he doesn’t speak the language, he doesn’t have any money and he doesn’t know anyone, and he takes your job on the first day – you’re shit, fuck off."
As a counterpoint: https://www.youtube.com/watch?v=LKrwhjOI8Nc (though 3blue1brown has a pretty different perspective on math in general, being far more focused on popularizing and teaching it as opposed to proving new theorems)
1. If it costs $6-22 million to produce a paper that the brightest minds in maths can't understand and use, this trend will stop soon enough on its own.
2. Why are these minds complaining that there are no authors to discuss the paper with? There are OpenAI researchers to talk to. If they refuse, because they themselves don't understand, then don't bother with it? You're responsible for your time. Write a response on what's unclear, and move on. What's the point of whining about others writing things you don't understand? See point 1.
3. If LLMs can be used to solve problems, that leaves more time for mathematicians to come up with follow-ups. That seems a great way to speed up the field, no? Just be sure you understand the solution before expecting anyone else to spend time on reading it.
I dont know what the future will hold, but in the past each time technology took over a profession, it ended up opening more doors than it closed. However the transition has always been rough.
I have faith that when AI settles, it too will open more doors than it has closed.
I don't know why there's so much drama. Animal human beings distracted from the real task at hand (eliminating poverty, hunger, human suffering) as usual.
Experts in fields are still required to validate the claims of AI. For mathematicians like Terry, people like him are still required to read through what the AI has come up with and confirm or create more experiments.
We don't yet live in a world with super AI hooked into everything and everything so it's not like AI can actually do anything with its new knowledge yet anyway. You cannot just hand those AI maths papers to anybody and expect them to understand what's going on. Nor can you expect the AI to find a revolution in fusion technology, send plans to its factory and have robots build a new type of fusion reactor because we do not have that level of integration yet.
But neither do we have UBI and we are still hurtling towards the hard ground of capitalism. This may resolve itself though because I'd imagine once we get proper AGI, the "meths" won't be able to keep it under wraps forever, eventually weights will leak, hardware will improve to where individuals can run them. Or an intelligent enough AI may decide to be benevolent and buy and run skyscraper greenhouses for those who are most in need.
> Much as one cannot unhear a movie spoiler or a crossword clue, one cannot explore a problem as profitably and richly once one is aware of an existing solution
Certainly, it’s like being made aware of cheat codes to video games: One doesn’t enjoy the game as much after but surely knowing something is true means you can find many other things that come from the pathway to it now that you know it’s true. Lots of science and tech is like this where someone shows something is doable and then people find better ways to do it but until that person showed it was doable there was no progress.
> I am horrified by the many person-years” of research, particularly by young mathematicians, “being casually disrupted or destroyed,” he wrote.
That’s what technology does. And he might be upset but we’re the ones paying for it and frankly, I’m happier to have more questions answered than for fewer answered but in an artisanal fashion.
Most notable is the fact that the released facts are like “treated waste”. But if the question was worth answering and the value is only in a good answer and not simply a correct answer, then the value has simply not been realized.
But that feels strange then that the value is in the good answer, not just a right answer and yet one finds oneself unable to go get the good answer because a correct answer exists.
The fact that any answers are made public at all is useful to us all. That’s free knowledge. Would it have been better if OpenAI had discovered this very achievable fact and not said anything? Surely the papers, post discovery would have spoken of the “hoarding” of such “essential human knowledge”.
> That’s what technology does. And he might be upset but we’re the ones paying for it and frankly, I’m happier to have more questions answered than for fewer answered but in an artisanal fashion.
Would you prefer if graph theory didn't exist but we could answer if you can pass all bridges in Königsberg, without going through same bridge twice?
Or if we could answer any question without knowing why? What about answering Hilbert without theory of Godel's Incompletness theorem? Or knowing Nth digit of Pi without calculus.
Because that's essentially what you're asking for. If you gave humans a Djinn that
could answer perfectly any question, it would kill most of our endeavors. Because it's not a problem that was unsolved for years "It's just the thing Djinn already answered so why bother?" Even if one is extremely curious, and devote a chunk of their life answering it, others would not see value in that curiosity. Because a Djinn can answer it in a few minutes.
Imagine you are Euler and magical Djinn's exist (that possess all mathematical knowledge written up to that point exist and function identical to LLMs). You ask it to tell you answer to the bridge riddle and it says that's not possible and even gives some plausibly sounding examples even. Then it throws a 11 pages of gibberish proofs at you, which are all true but very convoluted.
And what if you start digging into it? Won't other people say - "Hey Euler go back to ploughing the fields? We can have Djinn's answer all the math questions but this field isn't going to plough itself."
Today's, the Djinni-Euler's equivalent of someone looking at LLM's Navier Stokes equation proof.
Perhaps they would discover new Liquid Set theory that would turn Liquid dynamics from a field fraught with problems into a beautiful mathematically simple meadow.
> And what if you start digging into it? Won't other people say - "Hey Euler go back to ploughing the fields? We can have Djinn's answer all the math questions but this field isn't going to plough itself."
Seems like an overly pessimistic take to me.
If you have a magical Djinn happy to answer questions, why wouldn't you badger it a bit for the details? I can't imagine Euler of all people just wanted the answer.
It’s not pessimistic at all. Look at the advances in math thanks to hundreds years of pursuit to prove Fermat’s Last Theorem before Andrew Wiles finally did it in the 90s. You will not get that with LLM. That’s what mathematicians are mourning over.
This genie only knows the details that other people already formulated, because it doesn't actually think for itself, it just regurgitates human thought. That's what everyone seems to be forgetting.
Remove the human theorizing and the LLM won't be able to fill in that gap. All it can do is remix. It cannot formulate and, equally importantly socialize new mathematical theory. Without social acceptance and promulgation theory is meaningless. I might have a private "sort of graph theory but not" studying a slew of new mathematical objects called quizzgams, but if I cannot actually articulate this theory to anyone and get an active participatory body of people around it, it's pointless. Any "theory" an LLM can create de novo is such a theory. Because, again, it doesn't actually produce novel thought, just novel byte sequences. A thought is more than just its encoding, it is processual and social, which all the nerds and vc bros seem to not understand.
I’ve been on the other side of that, getting badgered for details by people who don’t have the conceptual frameworks to understand what I’m doing, and my experience is that it doesn’t really work. Sometimes, when they have a concrete goal in mind, they can communicate it to me and I can produce a demo showing that the software I’m working on achieves their goal. More often, they ask questions that don’t fully make sense, and can’t understand either my answers or my guidance towards the questions they should be asking.
If I were a Claude instance, rather than a software developer fielding these questions as a small component of my job, could I take a step back and instruct them from first principles until they do understand? Maybe. But maybe there’s just too big of a gap to be crossed in one step.
> I’m happier to have more questions answered than for fewer answered but in an artisanal fashion.
But the value in seeking mathematical answers was never in the answers themselves. It was in the things one discovers along the way, the questions asked, the tools developed. The artisanal fashion is the part that benefits non-mathematicians.
These AI proofs only serve as an I-told-you-so. They're not creating surrounding theory which can later turn out to have useful applications elsewhere.
> I’m happier to have more questions answered than for fewer answered but in an artisanal fashion.
Given that this is pure mathematics we're talking about, for the most part: Why?
Perhaps you are a mathematician and so these questions are relevant to you, but for most of us, these questions and their answers will not make any tangible difference in our lives or society.
Maths has made a very real and tangible difference to society. The easy, obvious, answer is online banking, which wouldn't work without crypto, which is pure maths. There are many more.
It used to be that Pure Maths got to affect the real world via Physics (and that odd thing where last decade's interesting mathematical exploration turned out to be the solution to this decade's Physics discovery). But t'internet consumes Pure Maths pretty much raw.
> The fact that any answers are made public at all is useful to us all. That’s free knowledge.
When mathematicians discover new results, they automatically become experts during the process, and then go around giving talks to explain their results, methods, and intuitions to other mathematicians. After years or sometimes decades of refinement and a healthy dose of serendipity, some of the mental frameworks percolate to other fields.
No one from OpenAI is willing to give a talk on any of their 300+ results because their machines have decoupled formal proofs from actual knowledge.
Right so this goes to the other alternative; there's still useful work for mathematicians after all in dissecting, distilling, and generalizing these results. But according to some we now inhabit an excluded middle where the AI produces useless results but also makes these problems useless for mathematicians to study further.
What exactly would you be advocating for? That LLMs can't be used to generate mathematical proofs? It's not even a case of intellectual theft, academic papers are in the public domain or can be accessed through a subscription.
What exactly would you want to regulate? And keep in mind that regulations are very effective at protecting incumbents, which, as of right now, also includes openAI.
If you invent the ability to tragedise a particular commons, and you also do almost all of the work of turning the crank to make the commons tragic, and then you sit there benefiting from the tragedy of the commons while saying “we may be profiting from it, but the tragedy of the commons is not our problem”, eventually we will figure out what you’re up to.
Is it useful to us all? I read thru the results list and despite years of college and graduate math classes only understood the statement of like five or ten. Prof Tao and his colleagues are able to spot the thing in their work that make faster imaging possible; are you?
Better approach: "holy sh*t, I can solve way harder math problems now". I bet openai would have loved to have Terry on their team leading the 'solve math' department.
If you use an LLM, you aren't solving a thing. Just as people who post about how "I built" some vibe coded thing are lying to themselves. You didn't do the thing, the LLM did the thing.
I can't lift a car, unless I use a jack. Mathematicians use theorem provers. Software developers use IDEs. Programmers would be pretty screwed if their keyboards had a 0 and a 1 on them and nothing else. Tools evolve.
Math culture optimized for thinking skills of proof-based understanding. Funding and education partly determined too. 3blue1brown did an analysis recently.
It is easy. We heard many angry programmers going ballistic about (un)maintainability of slop. That's the same, but very much more complex: imagine a large proof that maybe looks correct but it was written by a mentally unstable person that just committed suicide. What is its value?
I find it interesting that, several years ago when discussing AI, folks used to focus on how automation would first come for blue collar work. Things like driving being automated and truck drivers replaced. And then eventually on the horizon we would see things like this.
But we still have no self driving cars. Seems like the automation came by in the opposite direction. Perhaps driving will actually be the final thing automated.
While I agree with your statement overall, as someone who drives everyday in LA alongside Waymos without anyone inside of them I must disagree with this aspect of it.
We still have no general self driving cars. What we have is a bunch of geofenced tests. While we are closer than ever, we are still seemingly a long way away from truck drivers being obsolete was foretold over 10 years ago now.
A better formulation would be: we don't know if we have self-driving cars.
Because if it became fashionable for pedestrians to wear large green dresses with red balls, and everybody would wear that, we have no idea what the AI would do.
This is a general point rather than an argument supporting the GP comment, but it can be shockingly hard to know what the correct response to particular situations is, or predict how a system will respond. For example, one system I know had difficulty differentiating people laying on the road from unmapped speedbumps (particularly at night), but was very good at recognizing them standing up. Someone spent a lot of time testing with dummies until perception improved. Another had no idea how to handle people in fursuits and halloween costumes, because it was incorrectly applying animal behavioral models to pedestrians.
That's why the latest self-driving systems include reasoning models that draw from the massive amount of knowledge embedded in LLMs. Language evolved to communicate things that are not here and now after all.
Something I'm noticing a lot is that automation finds easy footholds in unregulated industries because there's no basis to push back on it. And there's a lot more tolerance for poor quality work in unregulated industries too.
An LLM automating web developers with 99% success rate saves the company millions of dollars and allows them to launch products and features faster.
A truck or a car that has a 99% success rate would be the top threat to society and quickly rise to the leading cause of death under 30 if widely deployed.
An LLM automating web developers basically puts the company out of business. Why would customers pay a developer when they can just build it themselves?
There are a lot of things that people are capable of doing themselves that they pay other people to do for them.
I agree that LLMs have and will continue to increase the number of activities that people can DIY. But I believe many people will still choose to pay for others to do things on their behalf.
“99% success” is too vague to be especially meaningful in such different use cases.
99% successful web development where the 1% missing is security that and the company leaks its entire repository of user data every few months is not good.
99% successful car driving where 99% of 5-year periods have zero accidents per car is an order of magnitude safer than the average driver. (And gut feeling, I suspect approaching the tail-end of the safest drivers on the road.)
>99% successful web development where the 1% missing is security that and the company leaks its entire repository of user data every few months is not good.
It feels like it's happening every Thursday and nobody cares. They just give people credit watch coupons or what's it called, and move on with their business. Worst case, a few pennies in fines.
Well 99.99% is you have a major data breach every decade or so, but there are lots of companies, so on aggregate across all of them it's every Thursday.
But if CVS leaks your purchases on a weekly basis, it's probably going to affect people's willingness to shop there. (Or at least to use non-cash.)
Exactly. Everything below L4 is _incredibly stressful_ and unpleasant to drive, because you have to be constantly aware and alert without having anything to do.
In the case of Tesla, daring to call such a system "Autopilot" is a breathtaking level of irresponsibility. You are responsible for the vehicle you are driving, practically, morally and legally, even if a companies' marketing and the system itself does its very best to divest you from that simple and obvious truth.
Pilots still are required to be able to take over immediately for an autopilot system and are responsible and accountable for all those items you list and more.
Calling it autopilot is precisely what it is, calling it self driving would be false marketing.
With this line of reasoning I can sell any car as a plane without wings. It flies, but only off a cliff, and doesn't land, but I only said it flies, not that it lands.
Most people expect other things from something marketed as flying, but specialists know that this is exactly how most things fly. And lawyers know to read the fine print.
/s and argumentum ad absurdum, sorry for eristic tricks.
> Everything below L4 is _incredibly stressful_ and unpleasant to drive, because you have to be constantly aware and alert without having anything to do.
Hasn't been my experience for the past year or so, give it a try sometime. Incredibly relaxing and frees up my mind to focus on potential hazards further than just one car length in front of me. Sometimes (don't hate me) frees up my hands/eyes to handle other things that need some temporary attention. Traffic jams, getting cut off by impatient drivers, being stuck behind slow drivers, none of it bothers me. I'm chilling out and talking to my kids and enjoying the scenery.
So basically, you're treating your Tesla as a Level 3 or Level 4 autonomous vehicle, even though its driving system is only Level 2. If you were endangering only yourself, that would be one thing. But you're also endangering other drivers sharing the road.
The "Autopilot" argument is ~5 years old. Teslas no longer have that feature.
The current FSD system has no relation to the old Autopilot, is enormously better, and very pleasant to use. A year ago FSD was nice, but I had to take over occasionally. This year it's much better, and I've yet to see a weakness, aside from some parking issues.
Self driving in a winter storm? Self driving in torrential rain? Self driving when mud covers a sensor it needs? Self driving if it hits someone? Pretty sure Tesla would say you were driving it then.
Driving is heavily regulated, and there are a million interest groups lining up to sue to stop self-driving. Imagine all the people who make their money from car crashes, for example.
Broadly speaking, this is proof that there will be no jobs coming after AI.
All past inventions have put some of the most miserable humans out of a job. Farming by hand is hard, so is copying books and don't even get me started on the dullness of making clothes by hand.
Driving all day isn't all that far off, though still much better than the above and definitely better than riding horses all day.
Telegraph operators? Hell no. Dude sitting in an elevator all day? No thanks.
It's always been from the other end. This time around, there's gonna be some 10-20 years of robot manufacturing, then a universal lifetime of robots fighting misaligned robots until enough paperclips have been manufactured.
Or you know, we block out the sun and live in caves or whatever you fancy.
I see your point but if self driving cars existed, worked like advertised and were economically viable they would and should be in every country in the world.
Developers are guilty of making reasonable projections based on contemporary industry trends, and they're getting slapped by unexpected revolution in computer science.
Yeah, as always in AI hard things are easy and easy things are hard. How many times have I heard condescending comments from programmers that radiologists are just about to be replaced by AI. And well, AI turned out to get kind of okayish at programming much faster than being acceptable at being radiologist.
The inconvenient truth is the “desk jobs” involving a human operating a computer are far easier to automate than piloting a physical vehicle through a complex environment… A desk job is doesn’t require lidar and cameras…
It was too easy to assume that an AI would never approach human intelligence and hence would only be used for “boring” jobs like driving.
I’ve long disliked the hype around AI but now see that human intelligence is perhaps slightly overrated, at least in terms of the loftier positions seemingly requiring such.
Claude Opus puts to shame any highly caffeinated “10x” software developer. Not saying it’s perfect, but damn good. It can knock out difficult code analysis/reverse engineering more than 20-40x faster than I can. There was even a time long before AI when people thought the same of me…
Hell, at this point, I’d rather deal with Claude than a low-cost offshore team that puts up crappy implementations with endless go-backs and rewrites. I say this from actual experience, not xenophobia. There likely are some high performing offshore teams, I just wasn’t lucky to have the chance of working with one. Have had a couple of local colleagues that were worse… Claude’s probably much cheaper too.
Unfortunately, the “knowledge worker” jobs historically tended to be higher paid.
On one hand, AI is a major asset to experienced professionals with access.
On the other hand, it robs junior engineers hard-fought experience - much like watching a movie instead of reading the book.
And longer term, I think the entire economic structure of society is going to change. Doctors, lawyers, software developers, engineers — none of these are safe from AI reducing the need for headcount.
human intelligence was always overrated, at least in terms of it's actual value to society. phds are often unemployed or "overqualified" for the roles they apply for, roles that pay the most are often roles which are less deskbound and more client-facing, roles that ai cannot replace.
alot of investment related roles, those require reading human emotions and pleasing people, a pretty face and pleasant demeanor with emotional intelligence helps more than raw iq.
Human level embodiment took 10,000x longer to evolve than human level abstract and symbolic information processing, and is also probably 10,000x harder to replicate in an alternative form.
One way to think about this is that the parts of our brain that are responsible for spatial reasoning and the basic automatic stuff we do day to day to just navigate the worlds are evolutionarily the most sophisticated and oldest. Evolution has so taken over this job that most of the time it's automatic and we don't even think about it, which makes it feel easy even though it's wildly complicated when you actually sit down and try to analyze and intellectualize basic stuff like navigating a 3D space in which almost anything can happen.
Intellectual pursuits are, by comparison, relatively new. Part of the reason they might seem so impressive to us is simply because we can't rely as much on eons of biological evolution, so even though what we are doing most of the time is really simple it seems "smart and sophisticated" compared to the far more complex mental operations that we are lucky are just automatic.
Think about it, you have an entire complicated as hell biological interior system that your brain manages continuously without so much as a conscious thought.
This is also why this hubris around the idea that LLMs rival human intelligence is quite laughable. If anything one of the major reasons they are so "great" is because they don't have to deal with a host of issues themselves (their computation is not responsible for keeping their bodies alive and hearts beating 24/7, data center ops takes care of that, unlike our computational system which, in addition to solving all these intellectual problems, also needs to regulate the body continuously)
I think fully automated driving is not so far off. Once the technofascists have their utopia, they will just allow full self-driving vehicles in every road in the country and the people will deal with it regardless of actual capabilities.
I am not surprised that this cage rattling of the academy landed on the front page of the NYT during this period of economic and political tumult. Mathematics can, and it should be an open question if it should, exist independently of provenance. I don't see mathematicians speaking with altitude about the economy of provenance; where AI may be dis-incentivizing mathematicians by eroding discovery claims; I see only entitled affront. But perhaps, if they are being honest, the glory of discovery is viewed as a critical motivator. If so, mathematics is thus imperiled by human vanity, not AI. The same logic applies to thinking and grappling with proofs -- it is a human choice to turn off your thinking. AI is attributed with false agency here.
I don't know if this will happen in math, but in other fields where computers have outstripped humans (chess and poker, for instance), there's been a loss of creativity, but there have also been other forms of creativity that take its place. There was a period of reeling where we had to figure out what it meant to just be able to know answers to the question that made the game fun, but there's also a moment of realization: just because a computer says something doesn't mean we can't make it our own. Using poker solvers to find creative non-equilibrium strategies can still be fun: the ingenuity comes from using the tools to think out side the box. Or, finding a nicer set of abstractions that explains why a strategy does a certain thing, and then starting to notice it showing up other places.
For math, just because we know a thing is "TRUE" doesn't mean the investigation is done. The folks that love math are driven by solving puzzles, and the puzzle is still there, only changed: instead of being "is this true?", the puzzle is now "why is this true?" Building theories, finding nicer proofs, etc: there is still plenty of room for creativity.
But in the meantime, it really is tragic that so many young minds have had their work stripped away from them.
Chess and poker as spectator sports have a high incentive to see humans compete fairly, and I think that's the reason why there are such strong anti-cheating measures (at least in chess; in poker, too, I suppose).
And the economy puts no such large incentives on much of the remainder of economically valuable work being purely human, quite the opposite actually. And instead of regulating the AI industry (which produces the "cheating tools"), they get trillions of investment. So this seems to be going in the opposite direction where it is actively worked against humans staying economically relevant.
Same as code, the llm can generate vast amounts and it seems to work, but no one understands the documentation Claude Code, or other LLMs, produce. Essentially, garbage because, to make use of it you need to be able to understand it, usually at a cost (unquantified), and if only LLMs do then what is the point?
It turns out it doesn't matter, because outside of a few narrow bands like Claude Code, no one cares what documentation an LLM writes for your project, because no one is ever going to go looking for someone else's project or library to solve their problem anymore.
So either an LLM decides to pull in your project as a library for reasons, in which the LLM can understand the documentation, or else no one besides the creator is using it anyway. So it doesn't matter.
Why would anyone use someone else's AI-coded project if they can get their own version that better fits their own needs in less time?
Sure you can make Claude produce documentation & code that is readable. You need to steer it and show it how you want it to write. When it gets it wrong, find counter examples so it can learn the style you want. Otherwise it's going to write what it thinks is best. What is best for LLM comprehension and efficiency is not necessarily best for the human.
It's interesting to see this all play out. Yes, on a personal level, it's a bummer for mathematicians that have the goal of figuring something out, and getting personal recognition and prize money. But now that AI can do this work better, I think we should mostly just celebrate that we can suddenly solve a lot of problems, and figure out how to use these abilities in a productive way. Math needs to change, just like software development has massively changed.
This is the language of someone who is blind to the reality of actual war. I’m sorry, you don’t have PTSD because computers got good at theoretical math problems, and part of the reason half our population looks down on elites is they talk like this to each people who got hit by an IED in Fallujah.
I do believe after the initial shock mathematicians will be able to use their math knowledge to solve practical problems, instead of lets solve this conjecture, prove this age old math riddle, how the pattern is possible. They may have some uses in fringe areas, but it doesn't seem all that useful. These guys are obvious quite brilliant, so when they combine it with other fields which they can branch to due to LLM's, they can still stay relevant. Ask your software engineer how that went.
IMO the most useful thing a mathematician can do is not solve “practical problems” but to come up with conjectures and riddles that look around several dark corners of math at once. The proving of a conjecture is a bit of a sport done to impress people with your cleverness; but the clever person was the one who made the conjecture to begin with.
Given the trajectory of LLMs to date I see them helping construct proofs for conjectures but not devising new conjectures of any material substance any time soon. The challenge is, as Tao has said elsewhere, part of being able to formulate a conjecture is by exploring the landscape around it by doing proof research. Seeking answers finds useful questions. The fear is the tools will take away the exploration of the landscape. But that’s silly IMO. It takes a special type of lazy to let a tool take away your understanding that’s important for what you’re goal is, and a special type of passion to learn with a powerful tool. The passionate will adapt and progress will accelerate, not slow down.
For instance Tao has posted some of his interrogations of proofs with AI assisted reasoning and it didn’t seem to diminish his ability to establish insight rapidly, but to shut down avenues rapidly and to pivot and expand his understanding rapidly. The insight was all his own, as was the path of inquiry. The understanding of the output was his as well. He carries it into tomorrow and uses it to formulate new more interesting conjectures the next day. The AI ceased to “exist” as soon as the inference turn was over.
The hand wringing is pointless and lame. John Henry moves aren’t necessary or useful, and when I see a tunnel boring project now I see tons of people well employed there, just the holes are bigger and better, and they’re engineers instead of strong backed hammer slingers.
Mathematicians might just be experiencing the first phases of the cycle of acceptance - resistance and anger, next is depression then eventually embracing it. Software developers as a whole are a bit further along the cycle.
"just". I think you should "justify" your use of "just".
Because it comes across as "ooh, you're just going through the five stages of grief, dummy! Look I've taught you psychology 101. Now that you know about grief, you might as well skip to the next cycle already. Support me on Patreon. Like, comment, subscribe"
Pointing out that someone is "just" grieving is not helpful.
I'm seeing this a lot in the past months of AI-for-math discussions. Had to get this off my chest.
Yeah, after I posted that I wondered whether someone would just focus on that word. You didn't just do that though, you went scorched earth - I meant no offense and sympathize with everyone affected by changes, I'm a developer and learning to embrace the change after a strong bout of existential crisis.
Math isn't useless. One of its defining features is its "unreasonable effectiveness" in formulating scientific ideas. It's hard to say exactly why it's so useful, but it is, even if mathematicians aren't trying to make it useful.
It's not at all clear whether the kind of math created by LLMs will retain the usefulness of the old math. LLMs are good at rigor but bad at intuition. It's not even really clear if the rigor was ever all that important. Theoretical physics is full of people using math in ways that don't meet the bar of rigor that mathematicians set for themselves, but they have enough physical intuition for what they're doing, so it doesn't matter. It's an open question whether post-LLM math will continue to supply scientists with the kinds of ideas that they need from it.
Terrence Tao was very supportive of AI and formalizing math with lean when it looked like it was giving ‘generalists’ like him an edge over mathematicians too deep into one particular niche field.
But now that it’s letting everyone, including mathematicians who are perhaps too specialized, explore ideas and patterns from related math fields, he’s suddenly ‘on a war footing’.
> basically both sides now dislike that he flip flopped
No, the dumb thing is the idea that there are "sides".
> basically both sides now dislike that he flip flopped
Literally the only people with this opinion of Tao are internet forum warriors who have no expertise in the field and who's opinion of Tao don't matter in the slightest.
> who's opinion of Tao don't matter in the slightest.
Similarly, Tao being ‘on the warpath’ does not matter in the slightest when it comes to formalizing math and finding proofs to important unsolved problems with AI.
“I’m on a war footing,” he said while grabbing coffee during a two-day math workshop at the University of California, Los Angeles, that was rife with talk about the existential crisis that artificial intelligence has created in his field.
So as every high schooler. That doesn’t mean much for actual results similar to what OpenAI “generated”, and doesn’t quite explain the “war footing”, does it?
We’ve yet to see the democratizing fantasies in math field to materialize.
Why so much resentment? To be a mathematician (I’m not one), you need to be relatively smart, hard working and passionate, considering it doesn’t usually pay well. These are admirable and aspirational.
If mathematicians were saying "the modern economy smashes the average person, and now we're in the same boat", I wouldn't be negative about them. But they aren't saying that. They're saying "our position of relative privilege is threatened and we must defend it."
What privilege? Did you miss the part where it doesn’t pay well?
Funnily enough, the understanding of modern economy is achieved through mathematics, developed by mathematicians and economists (using tools provided in math)
I don't think it is self-serving. Tao has stated plainly that he thought LLMs would go the route of assistants, like co-pilots. But what he feels now is that they are actually being engineered to be replacements. His claim is that the way OpenAI dropped these math results isn't "assisting" anyone, so we should all read between the lines.
Consider any man at his job, fighting the good fight. Your boss says "I've hired this man to assist you" and you are happy to finally have some help with your difficult task. Then one morning you come into work and see that the coming day’s work was done overnight by this other fellow. And the realization sinks in, he isn't there to help you, he is there to replace you.
In this view his reaction seems totally expected. I expect many professionals, e.g. doctors, lawyers, accountants, etc. will make this realization sooner or later. The companies are saying these tools will assist professionals, but in reality they are aiming to replace them.
you may not be aware of it but society largely runs on the results of maths, clueless indeed. and regulated or not, if there are financial savings to be made anyone can be shoved under the bus.
You might be mistaking my comment as a value judgement rather than an attempt to charitably explain the latest media communications from Tao. I detect in his position that some trust he granted the AI companies has been violated.
You are, of course, right that doctors, lawyers and accountants have more control over the environment they work in compared to mathematicians. But it doesn't change the underlying argument Tao is making. Your observation that those professions will react differently is likely to be true and only time will tell how effective their response will be.
But AI "assistants" is a marketing approach being made to all professionals at this time. Tao is implying this is a Trojan-horse strategy. If you let the assistants in without reasonable protections, you may lose control over the environment you are trying to protect.
> The companies are saying these tools will assist professionals, but in reality they are aiming to replace them.
If anyone doubts this, consider that Anthropic considers its TAM to exceed $30 trillion which is nearly the entire GDP of the US and 25% of the world GDP.
Only makes sense if they believe they will massively replace labor. Which, to their credit, they used to admit openly and publicly and only stopped because some crisis PR people told them "hey maybe you shouldn't say the quiet part out loud while the hoi polloi still have the power to stop this from happening".
You do realise Anthropic's management, after throwing its tantrums, gets a seeing to and has to do what its investors want? Which is pump up the valuation.
Do their own hiring practices reflect that ambition? They sure seem to be recruiting a lot of humans for typical roles in business, legal, and engineering. If they want to flex the power of their models to automate human jobs, why not lead by example?
> They sure seem to be recruiting a lot of humans for typical roles in business, legal, and engineering.
They have practically infinite investor money to throw at salaries (lost in the noise of how much they are spending on compute) so why not use it for now to reach their goal as fast as possible?
My thesis isn't that they have already achieved the ability to replace massive amounts of the labor pool, just that that has to be their goal given their stated TAM.
> If they want to flex the power of their models to automate human jobs, why not lead by example?
They don't want to flex this. They realized (after a false start) that it is better for them to avoid talking about this in public.
That doesn't mean their goals changed, they just realized that flexing before the goal is achieved could endanger the goal being achieved through political backlash.
>They have practically infinite investor money to throw at salaries (lost in the noise of how much they are spending on compute) so why not use it for now to reach their goal as fast as possible?
Wouldn't throwing that money into GPU be better because AI is smarter and faster ? So they would reach their goal even faster ?
I’m not making a claim one way or the other about the intent of these companies, but if your product made labor 3x more productive, you could still easily justify a TAM of the entirety of US GDP, without resulting in anyone losing their jobs. Obviously, here in reality, AI does act as a near 1:1 replacement for people in some roles, so we should expect some job losses. But I don’t think there’s any reason we should expect the entire US labor force to be automated away any time soon, even taking these assessments at face value
Tenured at age 24, I doubt he has any experience in industry to understand what he was getting into. Which makes me even more incredulous as to why people worship him.
The reason we fell first is because we embraced the copilots. We used them heavily, this gave them more and more training data on top of the code they slurped up from our using their assistants. Soon the assistant became the agent who killed the human.
They also had a rich starting point from open source code (which we somehow gave up without realising it). All of this won't happen as efficiently for these other fields, but it will happen, much in the way you've described. We (swes) turned out to be a rather dumb group of people, which is hilarious since we think we're clever.
The only moat we have is the human to human element, we need to talk to other humans in the business. Customers, etc. But once they're replaced by machines or automation, then machine to machine communication will be the preferred mode of communication and work and the legacy humans will be increasingly cut out of the loop. Human in the loop is a death sentence we just don't realise it.
Isnt OpenAI and specifically Altman openly talking about that being the goal?
> The companies are saying these tools will assist professionals, but in reality they are aiming to replace them.
They are openly saying that the goal is to replace humans and make humans obsolete. Like, literally openly. I am not saying I agree with that goal or find it realistic, but they do think so.
A few-minute search on Google shows that Altman has said a lot of contradictory things on the subject. A few quotes, as examples:
“AI won't replace humans. But humans who use AI will replace those who don't.”
vs
"Some areas in the job market will be 'just like totally, totally gone' as they're replaced by AI agents.”
and
“AI will probably replace most of the jobs people do today,”
The most recent position I could find says he has revised his earlier position on a total replacement due to the lagging adoption of AI in many industries. But I don't think there is a single position we can point to that they are "openly saying". It is fair to grant even the CEOs of these companies a change in position as they gain more information about capabilities and adoption, rather than insist that they hold, have held and will continue to hold fixed opinions.
The point is that Tao's understanding has changed. He may have been naive before, he may have heard in their words something he wanted to believe. Perhaps he was misled by people who he trusted that worked in the company. But now that he has more evidence, in the form of the maths drops and the way they have been handled, his suspension of disbelief no longer holds. The companies could have done this in a way that included mathematicians, so they chose not to. And that choice reveals their aims unambiguously in a way that a media-trained CEO or careful PR department can avoid.
That suggests that Tao is not being "self-serving" as others claim. He is saying that his optimism in the best-case scenario turned out to be incorrect.
I've never perceived him as 100% supportive. He has rather been open-minded about a new technology and exploring what it can do. Now it turns out it can destroy his field, so he's naturally against it (at least against the destruction, not necessarily against the technology)
I think ‘destroy his field’ is ‘destroy his method of being famous in the field’.
Terrence Tao is famous because of solving problems better that most mathematicians because he has an uncanny ability to look across different math fields. AI gets everyone this ability for 20 to 200$ per month, eventually free.
Most mathematicians are happy to see interesting problems in their field being solved, and are looking to build on these to find more interesting problems.
The point is to make the field progress by discovering new things!
Who gets credit for what and how credibility is assigned is going to be muddy for a while but that’s the case whenever a bunch of new science happens in close sequence. History is full of math/science discoveries having debated and dubious provenance.
I can't see how the field can even exist - not to say progress - if any problem can be solved before a human can understand it. Looks like mathematics without mathematicians, "progressing" in the same way as paperclip optimizer progresses in its productivity.
It provides deep insights into logic, computation, provides tools for us to understand the universe, establishes mind blowing relationships between seemingly unrelated things.
For example “how much information can a black hole contain?”
To whom? If there are no humans in the field, there is no one to get the insight. Maybe you are right, and there is just a new type of a mathematician being born, but as an outsider I just can't see what they could look like, what will be left for humans to contribute
Realistically, math will be done by well funded teams of people instead of cult of personality mathematicians.
Also, insights from scientific discoveries are for everyone. You do not have to understand the complex multi dimensional algebraic geometry of general relativity to appreciate that gravity bends time as well as space. You don't need to understand fifty years of linear programming research to use a modern solver.
> Realistically, math will be done by well funded teams of people instead of cult of personality mathematicians.
Most math is already being done by meagrely funded mathematicians. The entire US federal budget for mathematics is like $100M. One college football coach can already make 10 percent of that. No mathematician is making bank.
Is the implication of all this that mathematics research should get a cash injection to pay for high-powered computational tools?
> Is the implication of all this that mathematics research should get a cash injection to pay for high-powered computational tools?
Math will, sure. Mathematicians, doubtful. After all, most high end physics research with billions in funding is now done by postdocs making a lower middle class salary.
It remains to be seen if "any problem can be solved before a human can understand it". What if it turns out there are (many) problems too hard for both AI and humans.
It has been proved a hundred years ago that some problems can not be proven. So there are problems AI will not solve.
One might say, in the end, what's wrong with being self-serving? Are we _all_ meant to be self-sacrificing? Are we all meant to be the eggs that get cracked to build this wonderful future ommlette?
The TLDR seems perhaps tongue-in-cheek, but it's a worthy thought: the situation where our best experts find new science to be inscrutable is close at hand, if not here now.
Humans have been guilty of burying things we don't understand for millenia. Will we continue to do so "because AI"?
For me it just shows that modern math is not that important and mostly ego driven. If it was important, mathematicians would cherish the progress. I can't imagine bio researchers get mad that AI cured cancer.
It was devastating to learn in my late 20s that 99.9999% of what the average person does is based on personal ego and not a communal vision of the future.
There are plenty people in every discipline that prioritize their ego over measurable progress towards a stated goal - even less so a community focused goal.
Pure Mathematics is closer to philosophy or art than it is to empirical science.
In Pure maths, people are not generally solving problems because of some pressing practical need, it's purely out of intellectual interest, and if we're lucky there's some immediate practical application. More often, the knowledge sits in pure form for a while and years down the road some new invention, or practical consideration, or other field finds a useful application.
Just like literature and visual art, it serves an important epistemic and social function even in spite of its immediate lack of raw practicality.
You are very wrong about bio researchers! I am a mathematician who has worked in bioinformatics and, just like we're seeing with a few curiously well-placed-to-obstruct-progress mathematicians, are in it for power, influence, and credit and anything that erodes any of that is bad, bad, BAD!!!
> They “used math for what they needed, which was to evaluate their models,”
OAI first paper on the prize was a pretty shitty thing to do. But the rest of this looks like they are just mining the corpus and taking a brute force approach to do it.
Im going to say this again, the "pure math" academic types need to get a grip. Plenty of your peers got PHD's and happily made a fortune in finance, while screwing the world (See 2008 housing bubble) and none of you said a peep about that.
> Im going to say this again, the "pure math" academic types need to get a grip. Plenty of your peers got PHD's and happily made a fortune in finance, while screwing the world (See 2008 housing bubble) and none of you said a peep about that.
I would usually have been part of the downvoting brigade for this comment.
But to be honest the reaction from the ivory tower here is seemingly quite telling to a layman watching from afar.
It looks far more like this was some extremely gatekept community where you were only allowed to work on sanctioned things if so deemed worthy. Better not step one someone’s toes lest you get exiled! How much progress was lost due to newcomers never working on a problem due to told not to?
It’s starting to make those old timey Usenet kooks look a whole lot less crazy to me. They seemingly were right about this part.
Mathematics was funded and supported by a whole bunch of janitors and blue collar workers busting their asses to let entire departments of thinking men and women work on hard problems for the betterment of society. If it was just a super special friends club the whole time that was gatekeeping what amounts to a hobby, it’s going to me much harder to justify such a social contract.
Honestly not even sure what to think at this point. Extremely disappointing to me the more I read from these people.
I hope the LLM's will tackle theoretical physics next. If you think the math community is bad in terms of gatekeeping, and it is, the physics community is so much worse. Even community insiders are afraid to share their more unusual ideas at risk of becoming pariah's, outsiders have no chance. And that while they seem more or less stuck in their current track.
Admittedly it's also just really hard to come up with something better than the current track, but doing better has to start with being eager to explore different directions. Even if the new directions don't quite work just yet. And that eagerness just isn't there in the community, new directions are threats to the careers of sensitive people
Theoretical physics would, from my outsider view nowadays, benefit from an injection of vitality and an ability to tackle new venues. But the question is open whether LLMs can truly break new ground or if they work within the convex hull of current theory. And if that matters, too.
In the past there was too much activation energy to point out flaws in other’s reasoning. This is a natural response to slop cannons even prellms with misinformation shared.
Is Terence Tao just another AI booster nowadays, by the sheer amount of PR generating posts? Reading HN one might think that there is only a single mathematician in the world left.
I remember just last year he said the LLM were like incompetent assistants, but not completely useless. The tech advances are mind boggling just looking back at that.
In a world with better economic system, such progress in Artificial Intelligence and automation would have been viewed more positively, I mean who doesnt want to work less and have AI make rapid discoveries in scientific field. Instead we are filled with anxiety and dread of what will happen to our jobs and how we will survive.
I think there should be a political movement that retries socialism with AI. Basically nationalize everything and then automate everything. I think people could get behind that. Basically fully automated luxury communism.
I think there should be a political movement that retries capitalism with AI. Basically liberate everything and then automate everything. I think people could get behind that.
Good ole mass-starvation for the majority that can't find work that appeases the ownership class? It's a unique value-system I suppose.
Mass starvation was more of a communism thing, not accounting for wars.
Hilarious inversion of reality. Top marks.
A system where the humans value is tied to their ability to outproduce a massively more capable machine intelligence? How does that work, exactly?
Capitalism is already a planet-scale neural network optimizing a loss function: profit. The nodes in the network just happen to be humans.
Capitalism with AI would be exactly the same thing, but zero compassion (unless the AI has been trained for it).
Chile in the 1970s, anyone?
That was a scam or at least overblown in scope, the "control room" you see in pictures was basically a movie prop, and their idea was basically to connect that room to every factory/port/mine with teletypes, it's similar in spirit to what a modern stock should do.
Maybe if they haven't been bombed to death very soon afterwards, control room and everything, for trying to make things better for their population and kicking out foreign neocolonialists, would have gotten an update.
>nationalize everything
The government does not have an incentive to run anything efficiently as they cannot go bankrupt. Imagine if AI was run like the DMV.
Putting monopoly control of it in the hands of government also makes it extremely likely that whoever is in power will use it to manipulate public opinion + elections as well as encoding their political values into it.
What do you think a Trump-controlled AI would say if I asked about the war in Iran? We’ve already seen examples of companies encoding their beliefs into the system (see Gemini saying nuclear war is preferable to misgendering Caitlyn Jenner), imagine how much worse it would be if politicians were given control instead.
There will always be challenges, as is the case with any system. But I guess I don't really think LLMs will create a bunch of new jobs, so either we look into the future with gloom and doom as we who don't have wealth become part of a permanent underclass as opportunities continue to disappear, or we envision a utopia and work to realize it.
> Imagine if AI was run like the DMV.
I went to the DMV in Oakland and it was the most efficient DMV I'd ever been to.
Does the DMV have a reputation for being fast, efficient, or an enjoyable experience?
Personally I remember waiting for hours in a line wrapped around the building for the chance to take my drivers license test.
Another example: have you ever tried to interact with the IRS? The most nightmarish bureaucratic system I’ve ever had the displeasure of interacting with. And guess what my recourse is for them treating me like garbage? Nothing. A company, if they treat me poorly, I can take my business elsewhere. The IRS? The DMV? Not so much.
> A company, if they treat me poorly, I can take my business elsewhere.
Like Chevron, or Verizon, or Microsoft.
All of those companies are perfect examples of what I’m talking about.
Chevron: Exxon, ConocoPhillips, BP. From a customer perspective there are tons of competitors which make your life better ranging from QT, AMPM, to Buc-ees (a favorite which people literally LOVE to visit).
Verizon: Starlink, TMobile, ATT, Comcast, etc
Microsoft: Apple, Google, Cloudflare, Amazon (differentiates itself literally on quality of customer service)
The IRS or DMV? No competitor. Unhappy with their service? Go fuck yourself.
This is a very bad example.
The IRS is treating you bureaucratically and poorly because of lobbying from companies and politicians being bribed by said lobbyists.
My point being that you are beholden to a poorly functioning IRS because of capitalism; where companies have lobbied so hard against tax reform and simple filing that it more or less forces you to use their software.
I call the IRS and wait 4 hours on hold waiting to talk to a person. I get disconnected randomly and have to call back the next day only to have to wait another 4 hours. Finally I get in touch with someone and they are extremely rude, unhelpful, and treat me like garbage.
How is this somehow the fault of “capitalism”? Regardless of how the system is structured, the government has a near-infinite budget, they could theoretically staff the agency with enough people to answer my call in a timely manner. They could also train their staff to treat me with human dignity. They don’t do this, and the reason is that they have no incentive to do so. If I am upset by being treated poorly what recourse do I have? Nothing. In fact if I ignore their system long enough, armed goons will show up with guns and arrest me.
There are many examples of government agencies that have this reputation, not only in the USA but the entire world.
“Show me the incentive and I’ll show you the outcome” -Charlie Munger
IRS has been starved of resources following the "starve the beast" playbook.
Also the only reason we have to pay for Turbotax (etc) is due to lobbying. We had IRS Direct File for two years and it was great before being gutted by the current administration.
Your view of the DMV is outdated. There's been work put in around the country to modernize the system. I remember the hour long wait, but online reservations have made my last few visits in recent years take about 15-20 minutes
Prior to Republicans demanding the Post Office fund retirements in advance and various other hamstringing to other services US government was ridiculously efficient
They had to pass legislation to intentionally fuck the books to make them inefficient to fit their preferred narrative because government could be held accountable for inefficiency in ways private corps cannot.
You think people can get behind that? Like if Trump's US suddenly decided everything is state property and Elon Musk will be helping people automate everything, people will be like yeah that sounds good.
Nah not with Trump and Musk. It would have to be presented by a leftist, and maybe in a country outside the US.
There's no such thing. It'd be dictatorial as every other communist state ever was, and that's hoping the people in power wouldn't also subscribe to the communist ideas of killing a bunch of people to enable the revolution and to do it fast. Or read Terrorism and Communism (1920) and get scared - though most people end up thinking these mad men were nice grandpas.
> There's no such thing. It'd be dictatorial as every other communist state ever was, and that's hoping the people in power wouldn't also subscribe to the communist ideas of killing a bunch of people to enable the revolution and to do it fast. Or read Terrorism and Communism (1920) and get scared - though most people end up thinking these mad men were nice grandpas.
Oh come on.
Here's another thing to get scared about: AI and other kinds of advanced automation has the potential to completely undermine the attributes that made capitalism work for the vast majority of people. Rehashing dated mid-century anti-Communist propaganda tropes isn't going to address that. You're gonna need some fresh ideas.
Also people who want to seriously recreate the Soviet Union don't practically exist (outside of some irrelevant weirdos), except in the minds of some really indoctrinated libertarians.
Luckily our current authoritarian fascists are not showing any signs of preferring dictatorship over democracy.
Socialism CAN not work due to human nature. The sociopaths hijack the centralized assets while exterminating via reallocation all opposition.
And the micromanaging from a distance produces catastrophic results.
> And the micromanaging from a distance produces catastrophic results.
I think this has historically been true, but it is worth revisiting now with AI and general tech advancement. Might be more feasible now.
> Socialism CAN not work due to human nature. The sociopaths hijack the centralized assets while exterminating via reallocation all opposition.
You could also argue that capitalism CAN not work due to human nature. Just look at the state of climate change.
What makes you think socialism would handle climate change differently?
The socialism that did exist didn't take environmental preservation seriously and rather tried to silence reports about the damage.
> The sociopaths hijack the centralized assets while exterminating via reallocation all opposition. And the micromanaging from a distance produces catastrophic results.
Am I missing the sarcasm here? The difference from the current system would be...?
It's good that all of these benevolent billionaires are bestowing the world with the fruits of their goodness, and make sure that assets, knowledge and access to the market are fairly distributed. Their political involvement is to the benefit of all of mankind, and does thankfully not lead to the centralization of assets or power in one small group.
Well, so if its all the same- why not just say yes to cooperate-socialism? You just accept that the party (company) owns all the things and redistribute them as they see fit (for the benefit of all) - so wether the bossmann is called stalin or bezos- what difference does it make. Congrats, you got socialism speedrun- you are already at the disilusioned stage where you see the endresult. And thats still a efficient version, because the varous corporate-socialist empires have still to compete against one another. Now get in line critizen.
Michael Dell has been given thousands of children checking accounts. Musk just announced he will be giving children SpaceX shares etc....
Becoming a billionaire does not magically make you evil believe it or not.
On what basis do you think that's a good idea? This is a genuine question not a snide comment. I'm interested in your conception as to why it works for you. You're unlikely to respond here but maybe you or someone else will add a helpful link. I will admit that the idea does not 'compute' for me taking into account the nature of human beings - but I'm open to argument.
"Taking into account the nature of human beings" you mean humans' innate desire to help others, to share, to make friends, to spend time working together on shared projects / pursuing shared goals?
Or did you mean "human nature" (I'm using huge air quotes there) as you have experienced it in late 20th century / early 21st century United States?
>* the idea does not 'compute' for me taking into account the nature of human beings - but I'm open to argument.*
The current arrangement does not compute (or work), and gets us straight to doom, "taking into account the nature of human beings".
In the past I've been partial to a society based around self-actualization, like a liberal capitalistic society. However, with the way LLMs are progressing then I think society will turn increasingly technocratic and feudal, with no opportunities for social mobility. I don't really believe that LLMs will create new jobs or opportunities in the long run.
Historically socialism and central planning have been inefficient. With recent technological advancements it may be that the purported inefficiencies are no longer there, and I think a democratic, socialist government will be better at having the interest of the people than private for-profit monopolies. A society where everything is automated and you don't have to work could be pretty nice to live in.
But what about things where we still need humans, like food production, healthcare or construction and plumbing?
What about them?
What part of it wouldn't work?
Communism will work the moment communists understand options markets, specifically call options, which is to say that communism is impossible.
Curiously, capitalism will work the moment capitalists understand options markets, but in their case they need to also understand put options, which is to say that capitalism is impossible.
Progress in AI definitely makes the question of economic planification at a state level relevant again, at least for parts of the economy, be it for the disruption it causes to market economy (that was already showing lot of cracks btw) or the capabilities it gives to handle beyond human level complex systems.
In the book Red Plenty, on the Soviet economy of the mid 20th century, there's a section on an abortive attempt at optimizing the command economy using early computers and algorithms to have more effective production and distribution.
The attempt never materializes because some kindly clerk deliberately buries the letter from the enthusiastic engineer, who clearly does not understand that writing Stalin to tell him you figured out a way to build communism better than him, would be suicidal.
It's a fun counterfactual to think about, given that the vast bureaucracy needed for the command economy was one of its major limiting factors. Anyway, interesting book if you are into economic policy or quirky ways that systems can go haywire.
https://en.wikipedia.org/wiki/Red_Plenty
what kind of a Culture would that lead to?
I can see AI-automated logistics and production being popular. And AI-automated everything else being deeply unpopular.
Socialism failed so hard that the overwhelming majority of socialist countries recognized that socialism is inferior to capitalism, bailed, and adopted capitalism. Now that capitalism has brought about AI, socialists unironically suggest reverting to the inferior system, in hopes that it will have (magically) been rendered superior... by a product of capitalism.
This is the self-defeating contradiction at the heart of progressivism: it is a cult of good intentions. It doesn't matter if the promise of socialism has already been proved, on a global scale, to be illusory. It's the intentions that matter, and in their minds no amount of failure will ever tarnish good intentions.
I'm convinced that susceptibility to such pre-enlightenment "thinking" is a Great Filter.
AI isn't making math discoveries. It's generating a metric shitload of syllogism slop, whuch may or may not correspond to reality. We will probably never know, because really who has time for this bullshit?
Strange. In the article Tao mentions several mathematicians who had their problem solved by AI before they could finish their year long work.
Where they working on "slop"?
That's a big part of it, but I don't think it paints the whole picture. We are also losing the bits of work that were actually enjoyable. The challenge, thinking and creativity gave us something we enjoyed. Now we're like border collies in a world with no more sheep and now even the ball comes back by itself.
Another one that comes to mind is Marge Simpson in the Hank Scorpio episode where all labor in the house was automated and she turns to drinking out of boredom.
I'm fine with it as long as machines find the cure for hangover.
Or the Grey men in Momo (Michael Ende) who offer time savings through efficient appliances, while stealing the time made free through their use. Their main for is Momo, who encourages her fellow children to play for the sake of playing, which terrifies them.
It's a beautiful story, more and more relevant.
Is there any evidence that the thinking and creativity that we enjoyed has disappeared?
I'm firmly in the "programming is fun" camp, I enjoy thinking about the problems and solutions, but if I can get a LLM to deal with boilerplate then that's all the better for me.
I'm in the same camp, for the most part. But I also groan when someone checks in 60k+ LOC of vibecoded changes into production, without having any clue how it works. This happened to me recently. I was about start a fun module in the project, but then the other guy just pulled the rug from under me with claude and implemented the whole thing, then moved on. Not sure if I want to work under such conditions.
That's what I thought about 6 months ago: I'm a programmer, not a typist, so I'll just automate the typing part. There are a few problems with that:
1. AI agents aren't just typists. They'll fill in the blanks and implement something that works from extremely vague instructions and probably get it right too, because you and your users are predictable. You could be strict and throw out any changes that weren't explicitly what you asked for, but it becomes tiring and it will shape the way you think anyway. It becomes extremely tempting to increase the boundary of what you consider "boilerplate",
2. You probably have colleagues who don't like programming but please the managers because, of course, everything needs to get done right now, as soon as possible. Maybe one day we'll get organisations where enjoyment and understanding matters, but right now we've got tons of people who got in it for the money, just like to "build stuff" and don't care one iota about understanding (and they're oddly proud of this fact),
3. I'm starting to think the typing was a necessary limitation on output speed. I just don't think anyone can think as fast as LLMs can churn out code. You can easily get addicted to the speed and forgo understanding. Like point 1 this is insidious. If you're not really careful you just won't be able to keep up and before long you too will have a bunch of code you don't understand.
I disagree that what you're describing isn't just another angle of "broken economic system".
The broken economic system is the lack of perceived individual choice, and the priority of business decisions and business profit over individual satisfaction or autonomy.
If we lived in an economic system where maximising individual enjoyment and autonomy was priority, we could give AI to individuals to do with what they want. No sensible human/border collie would choose to give away the fun sheep herding part of their job if there weren't other forces and incentives at work.
But instead, AI is sold to businesses to profit, rather than given to individuals to do the right thing for everyone.
I don't think a system maximizing enjoyment would be any better. Why would anyone choose to work with sewage? Or why would most developers choose to align with rest of the team or with user needs, when programming is most enjoyable?
> I don't think a system maximizing enjoyment would be any better.
That's why I mentioned autonomy too. People like working and being valuable and choosing to add value. The issue is the current economic system doesn't consider things valuable if they don't directly generate a lot of money or profit for a business. An individual developer gets a lot of value from having a job they enjoy where they produce useful code that solves problems. AI removes some of that value for the individual developer whilst promising more profit and value for the business.
> Why would anyone choose to work with sewage? Or why would most developers choose to align with rest of the team or with user needs, when programming is most enjoyable?
Why do people choose to work with sewage now? They're not paid a lot. Programming is most enjoyable when it's useful. Writing code which is going to get thrown out because it doesn't align with your team is not valuable or fun, so why you or any other individual developer choose to do that given the choice?
As a hobbyist developer, I hate busywork. Boilerplate code is the bane of my existence, as is repetitive data entry. Forcing the demon at my command to do it for me so I can problem solve is far more enjoyable, and more efficient in terms of time. AI one-shotting problems is benefited by me thoroughly understanding and solving the problem with pseudocode in the initial prompt. I still do the intellectual work, but the LLM does the busywork.
Also, some things simply are not valuable within a system, regardless of the economic structures at play. Individual happiness is one of those things that has no value under any economic system, specifically because it is a moving target and follows Goodhart’s law.
> No sensible human/border collie would choose to give away the fun sheep herding part of their job if there weren't other forces and incentives at work.
It's not about giving it up, it's about it being taken away. You can't round the sheep up if they never leave the pen.
If something doesn't need doing then it's not work, it's a game. Many people enjoy decorating, but you wouldn't trash a room just to give yourself the excuse to decorate it. A few people might like programming just for the sake of it, but for most it was because we liked doing cool stuff that was hard. It's really important that it was hard.
If things aren't hard then it's just like doing the dishes: it's just time consuming and mildly unpleasant. There's no room for creativity or pride in doing the dishes. Nobody steps back, wipes the sweat from the brow and thinks, wow, that was hard, but I'm really proud of the result. Programming is becoming like doing the dishes.
Kennedy famously said we do things not because they are easy, but because they are hard. We need the challenge. We need it to be hard. If all we're left with is boring work like the dishes, or games, then we'll be like border collies left at home with endless treats and a ball. They can and do get depressed and we will too.
Progress in tech never implied working less.
It has always implied working less.
And not just implied: it has been a repeatedly openly made promise, from the start of the industrial age to today, repeated again and again, by scientists, journalists, technologists, futorologists, businessmen, even by sci-fi authors.
That mostly changes what people worked on rather than the total amount of time spent working.
In effect yes.
But the promise of less work, and more free time, has been there from the beggining.
In the early/mid 20th century they even had big discussions and books about what people would do with all the "leisure" time that was coming.
By implied I meant "caused". I did not meant "made people speculate that it might do something theoretically". Also, what sci-fi authors and futurologists write is utterly irrelevant here. We should distinguish fantasy and reality.
Practically, technological progress does not implies working less, it implies higher productivity. Which implies more wealth for "someone". Who that someone is depends on political system.
>By implied I meant "caused". I did not meant "made people speculate that it might do something theoretically"
That's on you. Implied doesn't mean "caused".
>Also, what sci-fi authors and futurologists write is utterly irrelevant here. We should distinguish fantasy and reality
A useless distinction, since what sci-fi authors were saying was taken to be a foretelling of things to come, adopted as such by many voices in the wider cultural space.
And of course futurologists were people who made (or attempted to make) informed predictions and even policy suggestions of things to come, not mere "fantasy" peddlers.
>Practically, technological progress does not implies working less, it implies higher productivity
That's your concept of it. Hasn't been historically the concept people (from technologists and journalists to politicians and sociologists) had of it. And even if it matches how things went, it's hardly the only way things could have gone (or should go).
>> By implied I meant "caused". I did not meant "made people speculate that it might do something theoretically"
> That's on you. Implied doesn't mean "caused".
It can mean both, actually (and usually someone insinuates something, not something, so I didn't find that this meaning of imply was a fit here).
So you mean a combine harvester should make you work more, not less?
> I mean who doesnt want to work less and have AI make rapid discoveries in scientific field.
A whole lot of people. Anyone who got into mathematics for love of solving problems (which I'm betting is most of them, as it's not like the pay is awesome) will be unhappy if they have the joy of solving problems taken away from them. Your argument here is analogous to saying "who doesn't want to have more children in the world without having to have sex to do it?".
It is not taken away from them and cannot be taken away from them. Just like you can solve any puzzle you like even if there is already a solution.
That’s not entirely true. There is joy in being someone who pushed the frontier of knowledge forward, even if only by a hair.
This is evidenced by the scant few people who get into math just so they can rediscover group theory or differential calculus on their own with no spoilers.
But how many people get to do that? For most people, math consists of solving problems to which a solution already exists.
Those people can use whatever.
The argument was about mathematicians, and "anyone who got into mathematics for love of solving problems".
Difficult to do that when you're unemployed, because machines took over your field.
We're not talking about doing it as a hobby.
You'll have to do something else for your income. That's how it is for most people who can't make an income from their hobby.
OK, so it IS "taken away from them" as their job, which was the point.
Or did you think the argment was that they'll be forbidden by force to do math, and come to refute that?
So mathematicians are no different from any other labor group that fights automation for their own benefit at the cost of overall welfare. Most artists are unpaid hobbyists, mathematicians should expect the same.
That would make society worse, not better. More people being unhappy and unfulfilled and underpaid is not progress.
Something tell me that at this point anyone saying stuff like war footing etc, against or for the AI (or anywhere in its immediate vicinity), are just doing it so that they can be one of the few who get benefited from it and are one of the few who also get to be in control and get to have power. Because they can see the writing on the wall and know that one either gets on this bus, or under it. A lot specialist creds/USPs are getting diluted every hour, every day.
It might also mean they came for you.
There's a whole industry of people on LinkedIn, preaching that I don't exist, that I'm obselete or worthless or deluded.
You get mad fast at the torrent of lies and "come to jesus" thinking.
Then they help themselves to your software.
> Because they can see the writing on the wall and know that one either gets on this bus, or under it.
good ol' TINA is back in town...
This isn't really a political problem. Politics is downstream of what we humans want, and more specifically what humans with power want.
The reason most problems aren't fixed is because you and I rather take our family to Disney Land than feed starving kids. We're don't vote for a political system which taxes us significantly more to try to stop people starving around the world. The problems Tao is worried about already exist for a large part of humanity.
You have two problems here:
1. You're not going to change the human incentive to care far more about their own family and friends and resist the government taking their assets to help the needy they feel no responsibility for.
2. In a world where most people are economically useless people ultimately have no political power. If you're not funding the government or contributing to it's maintenance then government ultimately doesn't need to care about what you want. You could go on strike or tell them you're very unhappy, but so long as the trillion-dollar AI companies are funding them and AI is running the government it makes no difference to them what people think. In fact, from their perspective, all you're doing is consuming resources. AI will likely create a new kind of resource-curse where wealth concentration will cause political corruption.
It's not about what we want, it's about what we believe. All you describe is enabled by beliefs systems, it's above rationalization. What you're describing is just learned helplessness.
On your second point, that rather assumes those 'unless' people will willing to just 'go away'.
That's typically not what happens - you either get bloody revolution or people just ignore the rules that aren't giving them a fair shot ( ie turn to crime - ie state disapproved activities ).
This is what has traditionally held back the elite from their worse excesses - they don't want to live in a world where either of those things happen.
ie what's the point of being rich if you are constantly worried about yourself or a member of your family is going to be violently kidnapped etc.
As to your first point - it's a bit like the first - if there is no social safety net, then it you could happen to you - you could get ill, lose your job etc. Even if you believe the system is created by total self-interest - then the past has shown that the equilibrium involves looking after everyone to some extent as:
1. It could be you one day.
2. Having lots of desperate people, even if it isn't you, is in no-ones self interest.
You seem to believe getting taxed is a choice people make. However, on the one hand economists like Zucman and news stories like the Panama Papers have proven the ultra-wealthy and politicians ("economically useful people") pay way less tax than regular people. And on the other, basically most people disagree with at least some of the uses of taxation, such as a war spending in the US. In fact, sometimes people get taxed without getting any benefits at all in return, such as during government shutdowns.
I think this all calls into question your basic premise that "politics is downstream of what we humans want", ie that the state is an emanation of the collective will of the people, which it serves. The facts fit equally well, if not better, an interpretation in which the state is independent of society and seeks to extract resources from it. This is also consistent with the Weberian state conception in which the state starts as the "stationary bandit" that collects taxes from a village to protect it from other bandits.
Your conception of "economically useless people" is also incoherent. Economic science is about how to distribute rare resources to maximize utility. These people are no less able to work and no less able to benefit from utility and are therefore not "useless" from an economic standpoint. I think you would benefit from just using words like "rich & powerful" and "poor & weak" which if I understand correctly is what you actually mean.
> I think this all calls into question your basic premise that "politics is downstream of what we humans want"
It only questions "the government is downstream of what we humans want". politics != government.
> This isn't really a political problem
What you're saying in this comment sounds _very much_ like politics, at least modern politics. There's been a few studies that suggest that people's position on the political spectrum is very correlated to their capacity for empathy for others (and in particular, strangers). First example I found on google: https://pmc.ncbi.nlm.nih.gov/articles/PMC10281241/ (note: I do not vouch for scientific rigorousness, I'm saying "some studies suggest that" not "it's proven that").
So:
> you and I rather take our family to Disney Land than feed starving kids
Speaking for myself, it's more true than false (although not that clear-cut). However:
> We don't vote for a political system which taxes us significantly more to try to stop people starving around the world
I sure do vote for that, as do a very significant portion of people. It's absolutely what I want, I am aware of my own biases (and other people's) to prioritise myself, and taxes are a good way to force this redistribution of wealth to happen despite these individual biases. That's kind of the whole point of the left, which is a very strong power in many countries (note: I'm not american and the "american left" is very different from other countries').
So "what humans want" is very much a political question: a very-much-reducted observation of the political spectrum is that it seems that right-leaning people want the best for themselves and their immediate social circle, whereas left-leaning people want the best for everyone.
I don’t think it’s about job security in the case of professional mathematicians. It’s about the fear of giving up the very thing they’re passionate about. It’s not like math researchers work on pure math because of the pay. If anything, they do it despite the pay.
I think you're wrong, and that's bulls*t. Something about virtue signalling.
Not just the pay, but motivation doesn't work on math insight alone. If you look from a distance it's clearly a mix of status, money etc. If what you say was true, many of them would be recluses up in the mountains, but none of them are.
LE. Think about it this way: if someone truly only cares about his ability to do "non-AI-contaminated" mathematics, nothing stops them from ignoring all the AI-related papers and just carrying on on his own. The thing that they are passionate about is not taken away by the field being more rapidly developed. What's being potentially taken away is the impact of their potential contribution.
Why wouldn't you just say bullshit? You didn't even write it in a self-censored format (e.g. bulls**t), you just wrote the actual word with a some funny characters in place of the actual letters.
Some online platform automatically censor or bring about negative repercussions for a given set of banned words. I realize HN is probably not among them, but I still formed this involuntary habit. You have a point tho. It does look much better in what you call self-censored format.
> If what you say was true, many of them would be recluses up in the mountains, but none of them are.
Except, for instance, Wiles and Perelman? And I’m pretty sure that mathematicians are rather more introverted and solitary on average than most people.
In any case, that just doesn’t follow. Mathematicians realize that collaboration is important in math just as it is in most other fields. Humans are also social animals and many of us enjoy collaboration and social interaction for its own sake. And yes, that means social status is a thing that motivates many humans. But nobody decides to study math in order to gain status! Any status stuff is entirely contextual to and conditional on having already decided to study math.
I maintain that you present a picture that's incompatible with how the human nervous system works. And that all humans are driven by the same biological mechanisms, all evolved by pressures to survive and reproduce. Mathematical beauty alone is not part of said pressures.
Humans are multi-objective beings.
Humans are built to focus on some objectives and not others at any given time.
Humans naturally prioritize objectives differently. Drives have exclusionary impacts on each other. In both real time and lifetime frames.
Reinforcing experiences further differentiate objective prioritization.
This leads people's behavior to be driven by entirely different net objective directions.
--
This diversity would be inevitable due to genetic diversity. But it is also a survival advantage.
Lots of studies show that populations maintain stable diversity of genes for entirely different life strategies, because operating differently from the majority is an advantage.
--
We don't actually have a "status drive".
We have drives that tend to generate status seeking behavior but can be subsumed by many different status-like pursuits, such as self-status of solving problems or completing single-person video games, being good at a hobby nobody else cares about, pleasing certain people even to the point of harming any recognizable definition of social status, acting to please (raise status with) internally generated or deceased personalities, a need to be contrarian or difficult to the point of low-social status but high internal status, etc.
--
Your assumption that same basic nervous system -> same net drives/behaviors, fails in much simpler species.
--
So no, mathematicians are no more motivation clones than they are genetic clones.
And mathematics is not a field that is attractive to people who give social status high priority, because it impedes social status.
It can be a mix of both. There's no reason, after all, that humans no longer being the most intelligent systems on the planet has to mean giving up such a passion, especially since it means living in a world with more and not less mathematics. One has to separate the joy of doing mathematics from a capacity (or, more importantly, need) to obtain a living doing it from the pride of being the best in your field.
It's interesting to recall Turing's own position: "There would be great opposition [to AI] from the intellectuals who were afraid of being put out of a job. It is probable though that the intellectuals would be mistaken about this. There would be plenty to do, i.e. in trying to keep one’s intelligence up to the standard set by the machines, for it seems probable that once the machine thinking method had started, it would not take long to outstrip our feeble powers. There would be no question of the machines dying, and they would be able to converse with each other to sharpen their wits."
On the other hand, Thomas Bernhard's The Loser is a horrifying account of the opposite standpoint---of an essentially second best piano student who cannot stand existing in a world with Glenn Gould.
A world where there are fewer humans who can ever understand math is the world with less mathematics.
What would such a world look like?
Mathematics represents the rational skeleton that upholds and stabilizes our vague, formless but far more common belief-based thinking.
Without it, losing it from neglect, we would collapse back into a pre-rational state of fantastical, wishful thinking.
Pretty much exemplified by large parts of US society already, but there is no bottom otherwise keeping society from collapse.
Well, it’s at least you and me thinking that.
> What would such a world look like?
Major religions, minor religions, cults will have a field day. Or more like a field century or a millennium or twenty, who knows.
Up to a few years ago, I would see or read some science fiction that was medieval times with spaceships (ala Dune) and I would roll my eyes and think “ffs, can’t people move on and invent something more original?”. Now I seriously believe that’s one of the most benign futures waiting for our species[^1]. Not that there aren’t lots of lights in this tunnel, it’s just that its shadows are very black.
[^1]: https://w.ouzu.im/aweb/unhinged
>It’s about the fear of giving up the very thing they’re passionate about
They have nothing to fear if that is their motivation. New players get into chess every year despite computer vastly outperform us.
Math is not entertainment though. It's one area where a sole human can do some of the most profound contributions to humanity.
Math is more like a treasure hunt than a chess game. Once the treasure is found, it's over. You can try chasing other treasures of course, but now you deal with superhuman competition (which will only become better with time). I can understand this is devastating and depressing
That’s exactly the fear: that math becomes just a meaningless game. Us mere mortals can get enjoyment from solving math puzzles whose solutions are well known, but it’s rather different being in the frontier, discovering entirely novel mathematical structures and proof techniques – and answers to questions nobody knows how to answer yet, sometimes even questions nobody has thought to ask yet!
Distinction without a difference. They happen to have jobs that they are passionate about. Many people do.
How can you say that? Even if their future livelihood were 100% guaranteed at the same or even higher level, the loss they feel would be the same. If you don't understand that, you probably just aren't empathetic enough.
Oh Brave New World.
Now that all of the trite and boring intellectual work is automated, I can look forward to having it bottle-fed back to me at night. Now get me a gramme in time...
I'm glad I'm not an Alpha, thinking so much is hard. Up and down is so much fun - what floor sir?
~ unnamed Gamma BNW elevator technician.
It seems that all AI can do, it can just "replace the average". Write an average quality software, do good enough business analysis, prepare mediocre report, do a bearable, but not so great translation, give you some basic medical advice, which is accurate 80% of time (but what if you are not lucky to have typical conditions?). It can also solve average difficulty level problems in math or physics.
That what it cannot do is to invent new drugs, cannot figure out cheap energy sources, find something better than Standard Model in physics, and anything that would contribute to overall human progress.
The result is that it can replace a lot of jobs, it will efficiently killed any research done and the level of master/PhDs, because majority of those can be done now with the help of AI (we already see this, the burst in new scientific articles - nothing groundbreaking, but publishable).
As a results we will have soon a gap, as only very determined people would go into science, analytical jobs, etc.
In one way, this is OK, we had too much science research that was done only for the sake of producing more "papers", we also had a lot of people in the companies doing "bullshit jobs".
But on the other hand, we might face soon situation in which there will be almost no people in Academia, so who will teach people, in addition, science worked often by doing wrong, unreasonable, crazy things, testing vague ideas and come up with something new and great. This required a lot of people doing science without any good results coming out, a lot of seemingly wasted effort just to hit several great ideas (a bit like Venture Capitals work).
This might also lead to decreasing number of white collar jobs. We can have a new "rust belt", the one for blue collar fall happened because of jobs offshoring, now we are "offshoring" white collar jobs to a few companies who offer AI models.
This all will affect badly society without any huge, visible benefits for it as a whole.
> It seems that all AI can do, it can just "replace the average".
That has not been my experience.
Because it's an oversimplification. AI proficiency is very spiky around tasks with well-defined reward patterns.
Solving Navier-Stokes and quasi-RH is “average” now?
I am not a mathematician, but from what I understand, mathematicians just do not not see this as progress. They see it as being robbed of potential progress. Mathematical progress is not achieved in the solutions to hard problems, it is achieved in the method of finding the solution. We are being robbed of the opportunity to find the solution by being handed the solutions.
This was a video I saw that covered this idea well: https://www.youtube.com/watch?v=KqiDqJMxg6o
I am also not a mathematician, but I think this is an assumption that people are making. It could be that by reading the solutions/proofs of these AI-generated results, those methods could still be discovered, ie. the AI could be discovering new novel methods implicitly. It's not exactly the same thing, but when the Navier Stokes blow-up "solution" came out, there was a lot of hoopla around it being stolen and not novel, but then once the dust settled, we had this:
> But closer examination reveals that OpenAI’s proof builds its unnatural force in a totally distinct way. The proof’s similarities to Buckmaster and Alpöge’s progress are superficial...
https://www.scientificamerican.com/article/openais-blockbust...
So I think more time needs to pass before a call can be made.
An interesting thought experiment is this: if we were to go back in time 150 years and tell our ancestors that Newton is just an approximation and give them a 5,000 page book about Special and General Relativity, QM and QFT, would we be robbing them? Initially the whole thing would be incomprehensible, but eventually they would chew through it and make sense of it. I don't really know the answer (and perhaps the analogy is not great since we're quite attached to our physics heroes from the last 150 years).
> those methods could still be discovered
there is a difference between "knowing" and "knowing about". "knowing" is having it deeply ingrained into one's intuition by working at a solution over years, often without progress in the immediate sense, and often without success in the absolute sense either.
Other than the person who developed the solution, everyone else will have to be "knowing about" it by studying written texts and lectures produced by someone else's mind.
That is the case many fields. Mathematicians, like physicists, are trained to develop a strong focus on methodology and intuition. It seems likely that the dynamic by which that intuition is gained will change.
> We are being robbed of the opportunity to find the solution by being handed the solutions.
I find this argument difficult to understand. As a math student in college with no ambitions (or realistic opportunity or aptitude) to pursue original contributions to the field, everything I learned was by definition already solved. Nevertheless I was able to - required to, in fact - work through each solution in order to develop understanding. And I did in fact learn by this method, as countless other students did before and after me.
So when I hear this argument from mathematicians, all I can hear is that they are frustrated at being out back into the position of being students, where the end result of the hard work of understanding is just the understanding itself without the prize of a new discovery. If they want to find the solution without reading it, they are still very much able to do so, just as their students do every day.
What is so hard to understand?
Difficult problem -> Developing new branches of mathematics to solve said problem -> solving problem, or failing to do so, it doesn't matter -> aforementioned new branches of mathematics are used to solve practical, real-world problems that benefit industry and economy.
The point of solving the problem is not the prize. The point of solving the problem is not even solving the problem. It is developing new methods and deepening understanding to drive useful applications.
> It is developing new methods and deepening understanding to drive useful applications.
Knowing that a solution exists is not an impediment to deepening your understanding of a problem.
For example: Knowing that there is a proof of Pythagoras’ theorem is not an impediment to thousands (millions?) of geometry students developing the intuition that comes from drawing the famous diagram where the number of squares visually add up to one another.
What about the existence of an AI-generated proof prevents a mathematician from working through the problem on their own to deepen their understanding, as if the proof didn’t exist in the first place?
That’s what is hard to understand.
> That’s what is hard to understand.
I'm baffled that you find the mechanics of human motivation hard to understand, (presumably ;) being a human yourself.
Studies have shown that people that know a certain piece of knowledge is stored somewhere, are less likely to remember said knowledge.
The sense (thrill?) of exploration and discovery can in fact be part of a person's motivation. The popularity of open-world games (often derided as 'walking simulators') are a testament to that. Do you really not see how that could be undermined by knowing that a problem that interests you is already solved?
there is a lot of thrill of exploration and discovery with things you already know to be true.
Basically all natural sciences work that way. Knowing the truth of an apple falling down a table when rolled over the edge is the beginning of discovery, not the end of it.
Mathematical discovery also worked more like theoretical physics 200 years ago. The modern way of formalization in maths might be dead now in some ways, but it's also only 100 years old. There's still many ways to do modern maths and have a lot of fun with it that are not taken away by AI.
> there is a lot of thrill of exploration and discovery with things you already know to be true.
it is qualitatively different
Because they've been through this process as part of learning math. e.g. you read your analysis book, and come to:
> If a set E in R^k has one of the following three properties, then it has the other two:
You stop reading, and you figure out the proof. Once you're satisfied, you continue reading the book and compare with its proof. The people who managed to get far enough that they were doing research have almost certainly gone through this exact process. They've self-selected as individuals who are able to motivate themselves to learn things even when they're already known, and to be able to figure things out without being given the solution. There's an insane amount of math to get through to get anywhere near the frontier, and it all builds on itself such that you can't just skim and skip, so they must have already learned to be able to do this.
Likewise, when given an exercise of the form "Prove P" or even "Prove or disprove P," you can be pretty certain 1. it is doable and 2. it is doable using techniques/theorems discussed in the course/book you're working through. But people are perfectly happy to do this for several years.
It seems like this whole argument is just rationalization to avoid saying "we think AI is bad because we wanted to discover things first!"
Think of it like a trip.
When you're learning/internalizing existing knowledge, you tread a defined path skipping unnecessary stops and diversion and heading instead directly to the destination. The destination, not the journey, is the point.
When you're discovering new knowledge in the form of proving/disproving, there's no defined path to follow, so there can be quite a bit of backtracking and diversions and detours into other areas you weren't planning on going initially and while there might be some well-defined paths to follow, you might have to cut your own path through uncharted desert or jungle.
All those diversions and detours make the journey just as if not more important than the destination because they create new destinations of their own for future travel that would not have been spotted or noticed for a while longer (if ever) otherwise.
So to bring it back to math, transitioning from having to develop proofs for theorems to validating/learning extant proofs completely changes the scope of future discovery. Everyone will tread the exact same path to a proof/theorem and then stand in the same place to look for future destinations and then use AI to build them a path to that new destination and then everyone will follow the same path to the new destination and repeat the process, so the chances of finding something curious along the way plummets. And something curious could be an entirely new field of math, or maybe just a new problem that isn't relevant to the intended destination but gives a view of many new never before seen destinations for future trips.
I think it's bigger than that. There's an unsaid anxiety around this that I don't think people are properly quantifying yet but is probably bubbling around inside their subconscious: we may soon get to a point where computers and machine intelligence outstrips our own and is able to solve mathematical and logical problems that are not just unsolved because they are hard but because we are hitting an inherent limit in the concepts and problems our physical brains can comprehend.
Demis Hassabis has talked about this a bit in regards to theoretical physics and it's an idea that I think I agree on. Every once in awhile we randomly get a super genius who's brain is seemingly able to conceptualise or visualise beyond the state of the art. But at some point I think we have to accept that we are just animals and inherently limited by our brains (and means of observing the physical world).
The scary part isn't that AI is solving the unsolved problems that will force people to act like students again. The scary part is that we may not be able to understand the work needed to get to the solution at all.
Obviously we're not quite to that level yet but it's entirely possible we do get there. And on the optimistic side ~ maybe that's what we need: better tools.
This reads to me like Victorian fears of buildings over three stories (you'll asphyxiate) or the idea that humans will die instantly when moving faster than a horse could carry you.
I see no reason whatsoever to expect that humans have any kind of limit to what we can understand as a species. We've had more unthinkable and incomprehensible discoveries than anyone cares to count. They become understood, normalized, and folded into our scientific canon. We went from inventing airplanes to landing on the moon in a matter of decades. We went from banging rocks together to quantum physics and string theory. I think we'll be alright.
Hypothetically, if a solution to a problem requires a billion intricate steps there is no way for humans to comprehend it. Human life span is too short. We can't even grasp what it entails. If a machine can pump out humongous proofs and solutions on a regular basis we will never catch up.
I'll add to it. The classic answer to your objection is "but as a species we'd have sooner or latter 1 billion steps worth of intellectual capital". Today someone gets to an intermediate result worth 1 million steps, tomorrow another million and so on.
But there's no guarantee that such "low IQ" intermediate steps exist. We do well with many classes of problems because of divide-and-conquer. But not all problems can be solved through divide-and-conquer.
For a rough analogy, see how AI plays chess and intermediate board positions often don't make sense to us. Imagine now an enormous chess-like game played in an enormous chess board where a match lasts longer than a lifetime and none of the intermediate steps make sense to any human.
I know what they are saying but it's really difficult for me to separate their job-preserving and peer-acceptence instincts from their opinion. I don't see how it couldn't be biased.
I remember a recent "100 hundred mathematicians on AI" post recently. Some of them appeared truly excited even if the majority wasn't. Who's right? Who's biased? I don't know.
I don't. Start with automating the jobs people hate, assholes.
Right now you're doing the equivalent of telling athletes that you've solved sports, and they need to sit back and stop playing so that we can enjoy progress in goal scoring.
We take discoveries in science and tech as they come, not as we would wish the universe and history offered us as.
Yes, we have to cope with the torrent of shit that's being pushed at us by misanthropic douchebags. It would be nice if they weren't degrading quality of life, but we just have to cope.
Thanks.
Nobody is misanthropic. Technology comes as it naturally does, new discoveries are more of a natural process than something any person can control. It just so happened that we got the automobile, it doesn't matter who was prepared for it or not, just the same with AI.
It's a little funny how quickly the conversation goes from "AI will never be able to {my-field}" before turning into "We cannot have AI ruining {my-field} with its obviously superior abilities"
If OpenAI had never made a push to get good at maths, we might still have a sizeable group of peopne stuck at that first line. I say that because I still hear in discussions the naive rebuttal "But we'll still need _someone_ to {one-step-up-in-hierarchy}" . Although you have to be curious now how long that sentiment can last.
The good news for those doing abstract maths might be that, now that OpenAI have proven that their AI can do the job in principle, there's probably not much left in it for them to keep going. Mathematicians should know better than anyone the lack of a direct profit motive in doing the work that they do.
(Edited for clarity)
I guess you didn't read the article? The end of it quotes Tao about how much more there is to discover in mathematics, and he expects humans using AI to get there.
My point was not that AI from now on should be done away with in mathematics research. I was rather commenting on the likelihood of AI companies continuing the "strip mining", as Tao put it, of his field.
Hacker news is not really a good place to talk about nuances involving academia. I don't expect VC minded hackers comprehend how someone can devote years of their lives working minimum wage trying to answer questions which earn them a fancy title on a piece of paper, for that matter.
Or hone their craft to best express their art and share their human experience
A lot of us here are VC minded hackers *because* we spent years of our lives working minimum wage jobs in academia and then eventually realized we preferred to build!
I am one of those. I'll also say I never felt the kind of emotion in software building that I did when working on PhD problems.
Or maybe to earn proper money?
> A lot of us here are VC minded hackers because we spent years of our lives working minimum wage jobs in academia and then eventually realized we preferred to build!
This is a disingenuous framing. I've "built" more in academia than in some jobs I had, and some VC-backed startups are renowned not for building but for their lack of ethics.
"Building" is not the discriminating factor.
Building things which you couldn't convince people to pay you for could be might as well building dubious crap
Man, majority of Sillicon Valley production is dubious crap with not much other utility or even actively harmful. And someone pays that.
Earning money is not curelated with usefullness these days. It is somewhat correlated with lack of ethics.
Reward alignment is the differentiator. Obviously it's very far from clear-cut what is worth funding in research. But i've seen a lot of crap research, that would have died off far sooner if it had some VC/free market equivelant.
Or preferred to eat. I love teaching, and I'm good at it. If it were more valued by society then I'd do more of it. As it stands, I'm in adtech, and I teach a little piano and math on the weekends.
I spent years programming for myself, for free. I did this because I loved it, not because I was interested in the VC game.
But you did something else for a paycheck in the meantime, right? They're talking about what mathematicians do for their meager paycheck.
> But you did something else for a paycheck in the meantime, right? They're talking about what mathematicians do for their meager paycheck.
Grigiri Perelman, who was awarded the Fields Medal, notoriously refused the prise because he stated no other recognition was needed.
A large fraction of people are open source contributors, hobby game devs, and various other types of people who fall under "devote years of your life with no formal remuneration"
The US-American mind cannot comprehend "free time" nor working hard on something just for the love of it and the joy of collaborating with other like minded people.
There's a reason that so many open source builders and contributors are unemployed people in social-welfare European states. There's a reason that nearly every great work in the English canon was written by someone who was on the dole at the time, from Nietzsche to Harry Potter.
It's not like you need to raise at least $5m to create an account here. There's a mixture of people.
The vast majority of users here are nerds first, business enthusiasts much later.
> obviously superior abilities
if you think that's the takeaway, you're not listening to any of the people affected by AI
I am myself one of them. This is just me doomposting as lightheartedly as I can muster.
> If OpenAI had never made a push to get good at maths
By snooping on work math researchers were doing on their platform and then overtaking them when sufficiently close to completion? isn't that what happened i'm not sure
No, as far as I know there's no evidence they used the other team's work for their own (and OpenAI changed their initial 'It's possible' to 'we double checked and it didn't happen'). What they did was hear a rumour about it and then spent millions of dollars on compute to scoop them.
That's not what happened. The claims of this for Navier-Stokes were already exagerated. It was dramatic but there was AI involved on both sides to make progress and the final proof did not use the same approach.
Finally, the list of hundreds of solved problems after that completely defeated any argument in that direction.
I don't think i disputed that LLMs were involved assuming that's how OpenAI would be able to snoop in the first place if the story is true.
Using LLMs doesn't mean some easy mode where humans don't do difficult work
so far it's been programming and math, the two fields most people would naturally assume computers would be good at :P
not saying it's not possible ai will continue to expand to more fields, but i don't think it's a coincidence that both math and programming are easily automatically verifiable. in fact for programming their effectiveness drops substantially once you remove any sort of testing or verification loop, and i imagine it doubly-so with math. try getting an agent to build something without any tests or verification, you'll see it go back to near-2024 levels. half of the work i do with agents is setting up a harness that can take and analyse screenshots, send direct input to the application, and compare results. this is something that should come standard with every harness.
if we can build automatic verification for more fields is a different and perhaps more relevant question.
> so far it's been programming and math, the two fields most people would naturally assume computers would be good at :P
If that is true, then only because "most people" have no understanding of what differentiates programming and math from "computation". Computers (as the term suggests) have always been extremely good at the latter, and useless at the former. It's only 2–3 years ago that computers, by way of LLMs, have started being good at the former.
I have to confess to being wrong in exactly that way in the past. On the other hand it is probably always good to behave as if the next step up in the hierarchy is still available. There's no point letting these things spoil your day twice.
Now I'm forced to think about it much more carefully. I don't believe that current LLMs can find every possible proof on their own from now on. I also agree that the PR returns have fully diminished. Given how hard it's been in recent years to fund e.g. a poorly paid postdoc, I doubt there's a ton of money lying around for getting the best models to work on mathematics problems. I think there's a chance we're heading into a really good era. I was able to make so much progress back when Google search was a useful research tool...
I'm of two minds about this. On the one hand, you get miraculous results with AI, and that is what you are referring to with "be able to {my-field}". On the other hand you regularly get useless, if not toxic, crap out of the miracle machine. If you work with AI, you know these moments: "no that is not what I meant at all!" [1] or "how could you have already forgotten the central motivation I laid out just ten back-and-forths ago?". We're calling this the jagged frontier, but the jaggedness itself is not the problem, it's how deep these cuts go into aspects that are important. These are, why AI is still not "obviously superior" in its abilities, can't replace mathematicians and software developers and lawyers and everyone else who is primarily working with text. (It's also why people say it is ruining their fields, instead of replacing them in their fields, because it only replaces some part of the work, and what's left is not tenable or pleasant (e.g. doing reviews all the time).)
Over all, I'm not quite sure whether I see these deep cuts occurring less and less with progressing AI. It might just be, that I'm giving them progressively harder tasks as well. But the fact of the matter still is that they aren't there yet and it needs proof they will get there ("there" being able to do competent work that is not strongly limited in their scale by human review and correction). So I'm still not convinced about the point you want to make, even though I see AI disrupting about every part of society, and am hoping for the benevolent super AI to lead us to utopia (and afraid of the cliff of human dictatorship on one side and extinction on the other).
[1] I've started to use these moment to reflect on whether a human in a comparable situation would fare better. Having only a few text inputs and small glimpses into a code base and knowing next to nothing about you or your project personally. Quite a few times I've concluded: No, they would not. But more than 50% they would, and also, these limitations are technological limitations of LLM, so you should probably not excuse them for that.
But isn't part of the problem that you simply don't have access to the hardware larger organisations do? OpenAI certainly run into the same constraints. but if they have access to terabytes of memory, while when you use the same model it's closer to 32GB, that will surely affect how the model behaves?
So the pain points you and I frequently run into, simply don't exist for a well connected individual(Sam Altman).
bullshit. such a machine would earn a profit no matter its cost, and Sam wouldn't be at the helm of a dog of a company that won't make it to 2030
Has OpenAI shared any new interesting _problems_? I.e. do more than strip-mine mathematics, as said in the article, but said: "Here is a question I cannot answer, it's interesting for this and that reason, I believe it's true for this and that reason, it's beyond me though, have at it." Has that happened yet?
AFAIK it has not happened.
Considering that this is where the mathematician excels over machine wouldn’t that only offer a new view from such a mathematician that “OpenAI has rapaciously stolen from mathematics that last dignity: of choosing worthy problems”? Perhaps with sufficient effort the community of mathematicians may yet forestall such an effort.
> wouldn’t that only offer a new view from such a mathematician
Don't invent things to get mad about, please.
They steal from the commons! They add to the commons!
+1 Good to know I’m not the only one!
This will be interesting to watch: Where will AI creating and solving problems in a loop lead to.
It'd be interesting if AI is great at solving problems but struggles to pose them.
This leads to the comment I've seen many mathematicians make that humans should refocus on understanding not just proofs and mechanics.
I'm in this boat too and I find it a bit strange that this hasn't been more emphasized by mathematicians themselves.
So far, a lot of the hullabaloo has been around solving legacy problems, but more interesting and more important for actually progressing mathematics is the generation of new insight and new problems. Someone had to pose all those problems OAI is solving in the first place, in some cases, ages ago.
The collective letter response to navier strokes, sort of touched on this, but still didn't really emphasize the epistemic value of problem generation explicitly. I find it sort of strange that this has been so underemphasized.
I think their expectation is that “problems” as we’ve understood them just won’t be nearly as important to mathematical research going forwards. The field will look more like e.g. economics, where progress sounds more like “developed our understanding of the microeconomic foundations of macro” than “breakthrough on the Coase transaction cost problem in five dimensions”.
I've never heard a particular reason why the Millennium Problems were of special interest. They had resisted solution despite significant effort, but I don't know if Riemann or Navier and Stokes had ever singled those out as especially high priorities. They started as ordinary problems and became known for their durability.
So I'm not sure if it's something we should expect from a machine, just because we don't expect it from mathematics either. Maybe the machines will interrupt that process because we've changed how we go about looking, but perhaps not because old problems are solved.
You've never heard a particular reason why they were interesting? Did you, say, check any information on the millennium problems?
From the very top of https://www.claymath.org/millennium-problems
In order to celebrate mathematics in the new millennium, The Clay Mathematics Institute of Cambridge, Massachusetts (CMI) established seven Prize Problems. The Prizes were conceived to record some of the most difficult problems with which mathematicians were grappling at the turn of the second millennium; to elevate in the consciousness of the general public the fact that in mathematics, the frontier is still open and abounds in important unsolved problems; to emphasize the importance of working towards a solution of the deepest, most difficult problems; and to recognize achievement in mathematics of historical magnitude.
It then goes into details in each of the chosen problems.
Everyone who built an identity on being the most intelligent in the room is going to have to come to grips with that no longer being a differentiator.
100%. We are moving to a time where do-ers will matter more than talkers.
Builders, please! Do-ers is not the preferred nomenclature, dude.
this isn't a guy who built the railroads here
According to whom?
Come now. You are using an LLM to perform as much of the work as possible/affordable. You're a User.
A wild thing to say about Terry Tao.
Was def not a slight on Tao. I consider him top tier in the math world.
lol
The only thing that will matter is capital, which will translate directly into all the talking and doing needed to make more money.
If your takeaway from all of this is that some other group of people has the special-est skill that can never be replicated by a computer, I fear you’re missing the point.
Ironic, given that all the alleged do-ing will be done by talking with an LLM.
How does that make any sense? Why do you assume that someone more intelligent would not be able to wield any AI tooling better than an average or below average human? Just curious if you're thinking short term or long term on this.
I mean, clearly "tooling" is not a perfect analogy for AI. As others have pointed out, if you pay money and get back a full website, app, game etc. it feels a lot closer to a service.
It's like asking why an expert pizza maker is not in a better position to succeed now that he has an excellent pizza delivery number he can call to have one available to his specification in an instant.
That's just a tool you rent and cannot own or make/improve/repair yourself.
This tool belongs to somebody (capitalist!) else and in a new world better tools will always win, not individuals anymore. And it feels like to go from being Rembrandt to CVS employee who takes passport pictures - result much better quality and cheaper but no skill and glory.
Interestingly, the dynamics strongly resembles the industrial revolution when from highly skilled manufactures society moved to factories with power machines. And it all came down who owns means of production. Now AI is a new means of production for all white collars jobs and if the industrial revolution taught is the way to go, nothing good will come out of it.
That’s like thinking that computers will belong to “capitalists.” It’s already clear that AI is going to be a commodity you’ll be able to rent for barely more than the price of electricity.
No matter how cheap it is, people will never be able to come anywhere close to affording what giant corporations can.
I'm somewhere in the middle on that. People used to think that computers would be owned only by large corporations, then home computers appeared and improved. It's getting tight now that logic scaling is mostly exhausted, at least with current operating principles. Even so, new specialized hardware and model improvements may help (for inference). Training seems to be the biggest problem, it seems hard to democratize.
And that's why Alta Vista still reigns supreme in search.
Yeah. Alta Vista died, and now there aren't any large corporations running search.
Nothing good for skilled labor you mean, especially in the short to medium term - just like in the industrial revolution. If the new technology is any good, it will produce desired things (let's say medical breakthroughs?) faster.
I don't particularly like AI, but if AI replaces developers and other knowledge workers, not everyone is worse off, and I don't mean just capital owners.
> Why do you assume that someone more intelligent would not be able to wield any AI tooling better than an average or below average human?
would someone who runs faster 100m also somehow drive better?
No, but someone who has trained their whole life to run fast, surely will be able to coach someone else to run faster than someone who has been on the couch watching television?
I use LLMs to great advantage, solving problems in my domain. I no longer make for loops.
> coach someone else to run faster
my point was that the new future where running faster doesn't matter any more might come, because everyone is driving (and potentially can't run much at all).
Would a rifle marksman be a better artilleryman than someone who never ever touched a gun?
See the beauty of analogies is you can make one to support any point.
but the analogy would be a riflemen trained to aim, and a person pressing button for guided missiles. How good you are at the original task is unlikely to matter when the new way supersedes the old way.
That's not how guided missiles work either…
so how does being a good shooter make you a better guided missile shooter?
Over someone who never fired any real weapon? Probably. You are not startled by violent sounds. You have intuition for ballistics, time to target, CEP, weather effects.
intelligence in its purest form was never a bottleneck for humans.
The social fabric that produces math got ripped up by marketing guys who didn't even bother to check their work.
He described it at 'strip mining', 'rude', and said that many grad students, who are given problems like these as a part of their training, had the rug pulled out from under them (because its customary to let people know you are working on something to prevent this kind of thing).
And your whole analysis is that Tao is worried about his 'identity', status, and 'being a differentiator'.
This is projection on your part. People have values that bear no resemblance to yours and it would behoove you to learn to recognize that.
Well they've been doing that to devs for a couple of years now and yet mathematicians seem to be much more vocal whingers (might be selection bias in the articles I'm reading though).
AI is coming for all of us knowledge workers, nobody is immune.
Um…us devs have been whinging with the best of them thank you very much.
The rug being pulled is the expectation of a reasonably high-trust ethical environment. The question to be asked is: What will graduate study look like in an utterly zero trust ethical environment?
If there is still such a thing as graduate study. If there is still such a thing as study. Tell me what to say to someone about to enter college about why it isn't a waste of their time.
yeah, let's all be stupid together
Most colleges, even before LLMs, were already a waste of time for most students. I mean they were somewhat effective for networking and economic signaling to employers but they had already lost the plot in terms of real value to society. And now with LLMs the entire education system will need to be rebuilt. Let's get to work.
Because learning is fun, useful and addictive all on its own?
This was already why people went to grad school. I think people weigh a complex bag of known and perceived motivations and risks. One of the risks is that your project gets "scooped." There were some weak ethical and practical safeguards around that. But completely rearranging the risk equation will change peoples minds about whether graduate study is worth it.
Disclosure: PhD, early 1990s. In my case, replicating my project would have required a sizable investment in equipment, much of it was purpose-built, among other things.
Interestingly we're a few months away from a data point on what happens to grad school applications.
Shitty. Why do you think people are complaining that AI is making life worse?
> He described it at 'strip mining'
Strip mining what, platonic reality? Mathematicians don't have a monopoly on mathematical truth. It doesn't exist for their benefit.
It doesn’t exist for OpenAI’s benefit either. The point of the “strip mining” analogy is that they are churning through the mathematical landscape in a way that optimizes for the number of problems solved rather than the amount of understanding of those problems.
But is understanding the end goal? Understanding for the sake of understanding? Or understanding for the sake of being able to solve problems for the benefit of humanity?
Yes, understanding is the end goal. That’s what defines the field of (theoretical) mathematics. There’s a separate field, called “applied and computational mathematics” or just “applied mathematics”, for research that focuses on computing concrete results.
What is the end goal? It's not making life better for humans, because we're posting about humans fucking hating this.
It's not about improving understanding, as you just pointed out.
So why? What the purpose? Is it just pure misanthropy?
Strip mining interesting conjectures. AI can answer interesting(pedagogically valuable, carrying important implications, etc.) mathematical questions in formally correct gibberish far faster than mathematicians can generate them. Until AI can replace the conjectures it resolves on its own, it's consuming a finite resource.
Will AI be unable to produce new conjectures?
Does creativity need sentience?
No. Genetic diversity and natural selection have created many intricate, beautiful, and useful structures. Unless someone is willing to argue that Darwinian selection is sentient, it's clear that theres at least one non sentient process that is creative.
The papers created by AI on math, right now, are torturous reads. Figuring out what is actually going on in them, is the work of months or even years.
I’ve seen multiple conference submissions that read like English, but take hours of effort to disentangle and figure out what they mean.
There is a limited number of known interesting problems that are worthwhile to engage in. New ones are found and understood, but it is a slow process and it is dependent on understanding and verification, not generation of content.
Saying AI will create new ones, strengthens the strip mining analogy. The idea that AI will find other problems parallels the idea that firms can cut down a forest and plant them elsewhere.
The conversation on HN is driven by non mathematicians, to whom math is a subject, like “nature”. It’s not their core business. The original post by Tao is a better source of information on what he means.
It can't consistently produce new, interesting-to-humans conjectures faster than it solves open problems, no. AI-generated natural-language proofs are more or less human-unreadable and are solely concerned with the process of constructing whatever object serves as the counterexample. Natural-language counterparts of formally verified proofs are often unfaithful to the formal component. All of this combines to create less-than-fertile ground for future study.
It is usually not the monopolist who is protesting against strip mining, it is usually the monopolist doing the strip mining and the environmentalist protesting it. Which is to say, I don’t think mathematicians are claiming a monopoly on mathematics, but I think AI might.
It's time for the social fabric of math to be ripped up, it's an industry being disrupted.
No one has the right to prevent others from working on a math problem. If you're working on a problem the best way to not get scooped is transparency: publish whatever you have as soon as possible.
Tao's behavior is most consistent with any other worker resisting automation for selfish reasons.
Tao is very prominently an early AI adopter. He, and other mathematicians, have fruitfully integrated it into their work. The way it is integrated matters, and it is carelessness and selfishness on the part of OpenAI that he is objecting to.
> It's time for the social fabric [of math] to be ripped up
This is the attitude of a social arsonist. You can, and should, integrate changes without maximizing destruction for its (or Altman's) own sake.
> an industry being disrupted.
This is the SV euphemism for law-breaking and monopolist practices in a country that has forgotten how to prosecute those with the most power and privilege.
> This is the SV euphemism for law-breaking and monopolist practices
Quite the opposite. The mathematicians are the monopolists who are upset that new-comers are able to do their job better than them, and even worse, they are giving it away to the world for free!
The horror! People giving knowledge to the world for anyone to use freely! Won't someone think of the oligopoly that was coordinating to make sure each of the gatekeepers get their slice of the pie?
Monopoly: Exclusive control of a particular market that is marked by the power to control prices and exclude competition.
Mathematics is collaboratively and publicly produced, it is vetted for free by peers, and results are publicly available. There is no 'market' and no 'price'.
These results, like the invention of LLMs, are often used by private companies for the generation of private profit.
"Open" AI used a private, unreleased, for-profit model to generate those papers.
What, precisely, did the mathematics 'oligopoly' gatekeep you, or anyone, from?
> their slice of the pie
There's very little money in academia, and even then, its a struggle to get any funding at all. What are you even talking about?
Final point, 'knowledge' is socially produced as well. Until the papers are accepted, they are machine artifacts that might be knowledge, but that same system you disdain will be what incorporates and validates those insights.
Until AI agents are embedded in glasses and everyone gets comfortable with sending their conversations to AI, the smartest person in the room is still going to be the smartest person in the room because they say smart shit. Or until the dumb guy types into their phone and says smart shit. Given the pushback to Meta's glasses, I think that'll be a differentiator for a bit longer still. Even before LLMs, you could check Wikipedia and different rooms treat the people that do that in different ways. And then there's the "Don't be a meat proxy" movement.
Not all rooms are real face to face. Smartest person also needs time to think and lookup information. Worst smartest person can think on one hypothesis at a time.
Intelligence is not knowing the answers to the questions, but knowing what questions to ask.
What? This is like a drive by shooting or something. Several PhD students almost certainly lost months of work, and others considering a PhD will have more doubts. Those problems aren't necessarily important because of the solutions, but because mathematicians can make unique contributions to mathematics in the process of solving them. LLM proofs haven't created any new mathematics techniques.
You think OpenAI is run by a bunch of idiots? Being the smartest person in the room is becoming exponentially more valuable.
Well, it's certainly headed by one.
Asshole and idiot are different categories.
Yes. If the early 21st century was the revenge of the nerds, this will be the undoing of that.
I made that comment a few days ago.[1] It saddens me. It may not be wrong.
[1] https://news.ycombinator.com/item?id=50036781
Revenge of the bot herds
Everyone who built an identity on earning a living doing useful work for other people is going to have to come to grips with that no longer being part of their identity.
No. It's just people who built an identity on the power that their intelligence afforded them. We view that power and the intelligence itself as the same thing, but they're actually separate.
I don’t think that is correct. For consistently good results, you need to set the right goals and be able to judge the quality of your outcomes. Even if you don’t do the hard work in between some thinking is required for non trivial work.
Humanity's entire thing is being the most intelligent in the room (of other animals). You take that away, what are we?
One version of the history of humanity is repeatedly, gracelessly, raging against the discovery that humans are not the centre of the universe.
Even without being the most intelligent we're still the ones driving mass extinction.
So there's that.
I'd still want the most intelligent human in the room to work with the AI. Ergo it's still a differentiator.
This is what Terence Tao's ChatGPT chats look like: https://chatgpt.com/share/6a5fdc7a-d6f8-83e8-bbea-8deb42cfed.... Can a layperson prompt the LLM like that?
"Garbage in, garbage out" is a polite way of saying the LLM's output is a reflection of the prompter's own intelligence.
You're out of date. The chats that found new Riemann conjectures were "look for a solution to the Riemann conjecture", followed by a bunch of "you can do it" and "I believe in you". The same goes for other breakthroughs, where the people involved didn't even know the math.
Yeah that's an interesting point of view. In my studies I got comfortable with the fact that there's always someone smarter than me.
At the same time it should be considered that with physical labor workforces lost their income source numerous times. Ironically they are currently being considered a safe haven.
It's still going to be a differentiator, in the way that being beautiful is still a differentiator after face filters were invented.
We know it's a filter, and we know it's an idiot parroting Claude.
It’s been interesting finding out just how many people in tech have the same chip on their shoulder as Syndrome, the villain from The Incredibles.
I just finished reading "Outsmarted: The Hidden Costs of Being the Smartest Person in the Room". Most of the HN crowd would resonate a lot with the points raised in this book.
The last(-ish) chapter does have a section on how AI has robbed the "cognitive elite" of our identity.
Elite pure mathematicians are like elite rock climbers or mountaineers. They desire the satisfaction of sieging the face or mountain and attaining first ascent[1], especially on faces that weren't considered humanly possible. It is an art form and there is much satisfaction and discovery in the process.
OpenAI is Doctor Octopus who just buzzed the climbers. They've proved there is a route, but so far can't explain it in a way that is intelligible leaving the climbers to catch up. Or is the AI making leaps of logic too complex or out of reach for the climbers a la the four-color-theorem[2]?
[1]: https://en.wikipedia.org/wiki/First_ascent
[2]: https://en.wikipedia.org/wiki/Non-surveyable_proof
I find it weird to blame OpenAI for using math as a benchmark. If they hadn't done so, then in three months, say, after releasing Bel, someone else would have used math as a benchmark for it (like mathematicians already do since Fable 5 and 5.6 Sol). The result would have been the same (hundreds of open problems solved quickly).
It isn’t a benchmark though. Not yet. They rely on mathematicians to check the proofs including all lemmas. And on other mathematicians checking the reviews. Without being on the OpenAI payroll of course. Now they have flooded the zone, overwhelming the review capacity of the whole field by at least one order of magnitude. It is the move of 15-year-olds holding tools they shouldn’t have access to.
LEAN.
Did they force anyone to focus on reviewing those results instead of other ones? People choose to focus on them for a reason.
I think it's always better to publish preliminary results early (as long as you clearly say so, and they did), and let mathematicians decide which of those are worth focusing on.
They did not do this in a vacuum. But it doesn’t matter much. Benchmarking needs a benchmark.
> The result would have been the same
No? How much did OpenAI spend on this and how many trials failed? I can’t imagine anyone not working for them can pay the absurd token costs!
But distributed over thousands of people, I see it happening. Maybe a bit slower, but still.
> distributed over thousands of people
Can you elaborate what does that look like?
A few people spend all their focus and tokens on one problem, and after some time I expect one of them to get at least closer to a solution. They can either work independently, or even better they team up and create a shared scratchpad for their agents. I don't see limits to scaling this, compared to OpenAI running however many subagents per problem.
And that multiply those few people by number of different problems.
We had to build the Torment Nexus, because otherwise, someone else would have built the Torment Nexus.
No, that's not what I say. My argument is that once the Torment Nexus is built, it is stupid to argue that they used it to torment people, when someone else would have tormented people with it anyway. If one wants to argue something, it's that the Nexus should not have been built.
And I honestly have no idea what Tao wanted to happen. How could you ensure that the AI "empowers" scientists and doesn't replace them. Intelligence is intelligence. If it's powerful enough, it will replace other intelligence.
> No, that's not what I say
Unfortunately, though, it is what you said. And more or less what you
> If one wants to argue something, it's that the Nexus should not have been built.
Or that it is being built in a way that is causing forseeable problems, while making no effort to anticipate and solve or mitigate those problems.
It’s more like: we had to build the Torment Nexus, because otherwise, people used its non-existence as evidence we couldn’t.
I very much wish they'd just let mathematicians have at it empowered by the model so we could all treat the people who claim they have a lean verified proof with an unintelligible explanation as the crackpots they are.
IIRC, Ramanujan[1] was given a book of Math results as a child and independently proved each result in a way that was original and often unusual and opened the field to a lot of discoveries. The Math establishment had a hard time wrapping its head around his proofs, like an alien genius, like an AI.
[1]: https://en.wikipedia.org/wiki/Srinivasa_Ramanujan
I feel that there are some surprising blindspots within this thread, in sympathy to mathematicians.
Don't we as tech ppl understand "purpose"? You might not feel purpose in their work, but surely you see how when it comes for your own, you might revisit why it is such an imperative that we give AI all tasks for want of speed and efficiency?
“Much as one cannot unhear a movie spoiler or a crossword clue, one cannot explore a problem as profitably and richly once one is aware of an existing solution.” He mourned, he added, “the path not taken, and the opportunities lost in the frantic race to develop this technology.”
This observation is so important. There is unintendedly something being taken away from us that cannot be given back. And it's a pure loss, there is nothing returned to us on an experiental level. It already existed before that "somebody else" would solve or discover something. Now this "somebody" is just just an alien nobody can relate to. And that "something" is everything.
Even if AI solves ageing, and climate change and whatever else; as humans we'll have lost something beautiful and precious. There will just be less of this sense of wonder and curiosity.
Sounds like the earlier feeling of trying to do software development in the age of having executives trying to move most of that effort offshore to "arbitrage the labor differential".
What if we meet extraterrestrial life? Would we ban them from showing us all the math they already solved and/or invented?
My gut tells me that we would be fine with that. LLMs are viewed differently by many people, and I can't decide whether people are so naturally opposed to these discoveries because the LLMs were manufactured by us (and should therefore be in someway inferior), or because the LLMs lack a 'soul'. It's a very interesting question to ponder.
LLM discrimination is so real!!
Have they solved the math by eavesdropping our conversations and taking the credit?
Greetings Earthlings. Here's some math stuff. In exchange, we own your planet now. We weren't asking btw. tnx.
My thoughts exactly. As far as I am concerned, super-intelligence that dominates pretty much everyone in mathematics already existed. Yet I didn't hear anyone declare that the existence of Jean Bourgain was a tragedy for mathematics. Why is it different when it's a machine or, as you mention, extraterrestrial life?
No, but the solutions they gave us would be pretty useless unless paired with understanding.
The societal rewards of the mathematical community's pursuit of answers to problems is not primarily in the answers themselves. It is in the practical problems that are eventually solved not by knowing the solution to the initial problem but by means of the new branches of mathematics that were invented to solve it.
Are you really unfamiliar with the concept that "the journey is the destination"? Read a book.
https://archive.li/0LTWn
the live video interview on numberphile comes without the New York Times' narrative filter
Highly recommend.
Link: https://youtu.be/bAnwMdfcMVw
One aspect that currently frustrates me is that even paying for the highest plans and spending multiple quotas across all flagship models, I still haven’t been able to reproduce any of the amazing feats Anthropic and OpenAI gush about.
I suspect their internal harness, models, and thinking budget far outstrip anything us peasants have access to (never mind the compute). So saying that they achieve all these headline results with 3 hours of GPT Pro is disingenuous. If that were so, hundreds of math phd students would’ve already recognized it.
I’m coming to the realization that my monthly subscription is only helping subsidize their real internal AGI, and my interactions are a small amount of human feedback and creativity which they can strip mine should they choose to.
Or is it possible they have entire teams dedicated to this effort? Building an internal “math platform”.
They have been nerfing the models for us plebs for a while now. Anthropic does the same, and if the Chinese models aren't doing this already, they will eventually.
It's hard to prove, but I'm personally extremely convinced of this. The point of AI (from the perspective of these companies) is to solidify and centralize their control of the economy and the world.
If you ask Qwen3.8 to give you a list of things it would refuse to help you do, it will list a number of things related to building/creating/training/altering LLMs. This didn't make much sense to me until I read that the #1 thing these frontier companies are optimizing their models for is training/creating/editing newer AI models. That makes a lot of sense to me now, and that's also something which they will want to keep 100% under wraps.
Therefore the #1 focus of their research and efforts and expenditure will be something that they don't want any of us to get access to. I think many other behaviors like model nerfing follow from that. It helps explain these frontier research products which we ourselves cannot get access to.
“They took’er jobs!”
Funny when it’s someone else eh?
Just learn a new trade Terry.
(I am kidding if it wasn't obvious)
'Ey 'ook 'e' 'obs!
Hurr durr durrr!
the rallying cry 10 years ago was "learn to code" ironically.
Jimmy Carr in 2008:
> Of course you get a lot of right-wing people saying "oh these Poles; they come over here taking our jobs". I think if a guy from Poland arrives and he doesn’t speak the language, he doesn’t have any money and he doesn’t know anyone, and he takes your job on the first day – you’re shit, fuck off."
https://www.youtube.com/watch?v=t2ICmOYP8gs
Somehow I think "taking our jobs" concerns are going to be a lot more palatable.
That was always a dumb argument.
If the pole is willing to work for a third of the price the local(I'm assuming Englishman), of course it is detrimental to UK labour.
Pretty good for the capital owning class, though.
Speaking of capital owning, Pole and pole are two different words, as are Polish and polish.
As a counterpoint: https://www.youtube.com/watch?v=LKrwhjOI8Nc (though 3blue1brown has a pretty different perspective on math in general, being far more focused on popularizing and teaching it as opposed to proving new theorems)
I must be missing something.
1. If it costs $6-22 million to produce a paper that the brightest minds in maths can't understand and use, this trend will stop soon enough on its own.
2. Why are these minds complaining that there are no authors to discuss the paper with? There are OpenAI researchers to talk to. If they refuse, because they themselves don't understand, then don't bother with it? You're responsible for your time. Write a response on what's unclear, and move on. What's the point of whining about others writing things you don't understand? See point 1.
3. If LLMs can be used to solve problems, that leaves more time for mathematicians to come up with follow-ups. That seems a great way to speed up the field, no? Just be sure you understand the solution before expecting anyone else to spend time on reading it.
https://archive.ph/kD622
I dont know what the future will hold, but in the past each time technology took over a profession, it ended up opening more doors than it closed. However the transition has always been rough.
I have faith that when AI settles, it too will open more doors than it has closed.
I don't know why there's so much drama. Animal human beings distracted from the real task at hand (eliminating poverty, hunger, human suffering) as usual.
Experts in fields are still required to validate the claims of AI. For mathematicians like Terry, people like him are still required to read through what the AI has come up with and confirm or create more experiments.
We don't yet live in a world with super AI hooked into everything and everything so it's not like AI can actually do anything with its new knowledge yet anyway. You cannot just hand those AI maths papers to anybody and expect them to understand what's going on. Nor can you expect the AI to find a revolution in fusion technology, send plans to its factory and have robots build a new type of fusion reactor because we do not have that level of integration yet.
But neither do we have UBI and we are still hurtling towards the hard ground of capitalism. This may resolve itself though because I'd imagine once we get proper AGI, the "meths" won't be able to keep it under wraps forever, eventually weights will leak, hardware will improve to where individuals can run them. Or an intelligent enough AI may decide to be benevolent and buy and run skyscraper greenhouses for those who are most in need.
> human beings distracted from the real task at hand (eliminating poverty, hunger, human suffering) as usual.
We've already had this solved for a long time, but nobody has implemented it yet. Automating math isn't going to get us closer.
War against who? You don't need to make enemies out of things where you can avoid.
> Much as one cannot unhear a movie spoiler or a crossword clue, one cannot explore a problem as profitably and richly once one is aware of an existing solution
Certainly, it’s like being made aware of cheat codes to video games: One doesn’t enjoy the game as much after but surely knowing something is true means you can find many other things that come from the pathway to it now that you know it’s true. Lots of science and tech is like this where someone shows something is doable and then people find better ways to do it but until that person showed it was doable there was no progress.
> I am horrified by the many person-years” of research, particularly by young mathematicians, “being casually disrupted or destroyed,” he wrote.
That’s what technology does. And he might be upset but we’re the ones paying for it and frankly, I’m happier to have more questions answered than for fewer answered but in an artisanal fashion.
Most notable is the fact that the released facts are like “treated waste”. But if the question was worth answering and the value is only in a good answer and not simply a correct answer, then the value has simply not been realized.
But that feels strange then that the value is in the good answer, not just a right answer and yet one finds oneself unable to go get the good answer because a correct answer exists.
The fact that any answers are made public at all is useful to us all. That’s free knowledge. Would it have been better if OpenAI had discovered this very achievable fact and not said anything? Surely the papers, post discovery would have spoken of the “hoarding” of such “essential human knowledge”.
Overall, I find the thing unconvincing wholly.
> That’s what technology does. And he might be upset but we’re the ones paying for it and frankly, I’m happier to have more questions answered than for fewer answered but in an artisanal fashion.
Would you prefer if graph theory didn't exist but we could answer if you can pass all bridges in Königsberg, without going through same bridge twice?
Or if we could answer any question without knowing why? What about answering Hilbert without theory of Godel's Incompletness theorem? Or knowing Nth digit of Pi without calculus.
Because that's essentially what you're asking for. If you gave humans a Djinn that could answer perfectly any question, it would kill most of our endeavors. Because it's not a problem that was unsolved for years "It's just the thing Djinn already answered so why bother?" Even if one is extremely curious, and devote a chunk of their life answering it, others would not see value in that curiosity. Because a Djinn can answer it in a few minutes.
Where's that from?
Now math isn't my wheelhouse, but every LLM I've seen provides far more than just the final answer and is quite willing to answer questions.
It's from this: https://www.youtube.com/shorts/afLSVRFzsFc
Imagine you are Euler and magical Djinn's exist (that possess all mathematical knowledge written up to that point exist and function identical to LLMs). You ask it to tell you answer to the bridge riddle and it says that's not possible and even gives some plausibly sounding examples even. Then it throws a 11 pages of gibberish proofs at you, which are all true but very convoluted.
And what if you start digging into it? Won't other people say - "Hey Euler go back to ploughing the fields? We can have Djinn's answer all the math questions but this field isn't going to plough itself."
Today's, the Djinni-Euler's equivalent of someone looking at LLM's Navier Stokes equation proof.
Perhaps they would discover new Liquid Set theory that would turn Liquid dynamics from a field fraught with problems into a beautiful mathematically simple meadow.
> And what if you start digging into it? Won't other people say - "Hey Euler go back to ploughing the fields? We can have Djinn's answer all the math questions but this field isn't going to plough itself."
Seems like an overly pessimistic take to me.
If you have a magical Djinn happy to answer questions, why wouldn't you badger it a bit for the details? I can't imagine Euler of all people just wanted the answer.
Well you could, but would it produce its own unique theory just to simplify for people? Probably not. It definitely didn't do it for Navier Stokes.
It’s not pessimistic at all. Look at the advances in math thanks to hundreds years of pursuit to prove Fermat’s Last Theorem before Andrew Wiles finally did it in the 90s. You will not get that with LLM. That’s what mathematicians are mourning over.
This genie only knows the details that other people already formulated, because it doesn't actually think for itself, it just regurgitates human thought. That's what everyone seems to be forgetting.
Remove the human theorizing and the LLM won't be able to fill in that gap. All it can do is remix. It cannot formulate and, equally importantly socialize new mathematical theory. Without social acceptance and promulgation theory is meaningless. I might have a private "sort of graph theory but not" studying a slew of new mathematical objects called quizzgams, but if I cannot actually articulate this theory to anyone and get an active participatory body of people around it, it's pointless. Any "theory" an LLM can create de novo is such a theory. Because, again, it doesn't actually produce novel thought, just novel byte sequences. A thought is more than just its encoding, it is processual and social, which all the nerds and vc bros seem to not understand.
I’ve been on the other side of that, getting badgered for details by people who don’t have the conceptual frameworks to understand what I’m doing, and my experience is that it doesn’t really work. Sometimes, when they have a concrete goal in mind, they can communicate it to me and I can produce a demo showing that the software I’m working on achieves their goal. More often, they ask questions that don’t fully make sense, and can’t understand either my answers or my guidance towards the questions they should be asking.
If I were a Claude instance, rather than a software developer fielding these questions as a small component of my job, could I take a step back and instruct them from first principles until they do understand? Maybe. But maybe there’s just too big of a gap to be crossed in one step.
This reminds me of the X Minus One episode "A logic named Joe".
https://www.youtube.com/watch?v=HQuH5nI-pHQ
> I’m happier to have more questions answered than for fewer answered but in an artisanal fashion.
But the value in seeking mathematical answers was never in the answers themselves. It was in the things one discovers along the way, the questions asked, the tools developed. The artisanal fashion is the part that benefits non-mathematicians.
These AI proofs only serve as an I-told-you-so. They're not creating surrounding theory which can later turn out to have useful applications elsewhere.
> I’m happier to have more questions answered than for fewer answered but in an artisanal fashion.
Given that this is pure mathematics we're talking about, for the most part: Why?
Perhaps you are a mathematician and so these questions are relevant to you, but for most of us, these questions and their answers will not make any tangible difference in our lives or society.
In which case why are we funding mathematicians?
Maths has made a very real and tangible difference to society. The easy, obvious, answer is online banking, which wouldn't work without crypto, which is pure maths. There are many more.
It used to be that Pure Maths got to affect the real world via Physics (and that odd thing where last decade's interesting mathematical exploration turned out to be the solution to this decade's Physics discovery). But t'internet consumes Pure Maths pretty much raw.
Why? Philosophical position: https://wiki.roshangeorge.dev/w/Observation_Dharma
> The fact that any answers are made public at all is useful to us all. That’s free knowledge.
When mathematicians discover new results, they automatically become experts during the process, and then go around giving talks to explain their results, methods, and intuitions to other mathematicians. After years or sometimes decades of refinement and a healthy dose of serendipity, some of the mental frameworks percolate to other fields.
No one from OpenAI is willing to give a talk on any of their 300+ results because their machines have decoupled formal proofs from actual knowledge.
Right so this goes to the other alternative; there's still useful work for mathematicians after all in dissecting, distilling, and generalizing these results. But according to some we now inhabit an excluded middle where the AI produces useless results but also makes these problems useless for mathematicians to study further.
Yes there's still useful work only mathematicians can do, what is the incentive system that encourages them to do it? Currently, none.
This is not OpenAI's problem.
It's their problem if we make it their problem.
edit: lest this be misconstrued, it can become their problem if it is wildly unpopular and undesireable behavior is regulated away.
I advocate for this path.
What exactly would you be advocating for? That LLMs can't be used to generate mathematical proofs? It's not even a case of intellectual theft, academic papers are in the public domain or can be accessed through a subscription.
What exactly would you want to regulate? And keep in mind that regulations are very effective at protecting incumbents, which, as of right now, also includes openAI.
And thus, the Tech Bro has reached the final stage in its developmental lifecycle.
"Burns down the societal structures for gaining mathematical knowledge"
"Not our problem lmao, our IPO valuation went up"
The Asshole’s Lament
If you invent the ability to tragedise a particular commons, and you also do almost all of the work of turning the crank to make the commons tragic, and then you sit there benefiting from the tragedy of the commons while saying “we may be profiting from it, but the tragedy of the commons is not our problem”, eventually we will figure out what you’re up to.
This is hyperbole at best. Let's try another take: Should a new company making flying cars care about the economic fortunes of tire manufacturers?
Look at programmers, we took it in strides
talk for yourself
Is it useful to us all? I read thru the results list and despite years of college and graduate math classes only understood the statement of like five or ten. Prof Tao and his colleagues are able to spot the thing in their work that make faster imaging possible; are you?
Better approach: "holy sh*t, I can solve way harder math problems now". I bet openai would have loved to have Terry on their team leading the 'solve math' department.
It's telling that isn't his response.
If you use an LLM, you aren't solving a thing. Just as people who post about how "I built" some vibe coded thing are lying to themselves. You didn't do the thing, the LLM did the thing.
I can't lift a car, unless I use a jack. Mathematicians use theorem provers. Software developers use IDEs. Programmers would be pretty screwed if their keyboards had a 0 and a 1 on them and nothing else. Tools evolve.
Theorem provers don't generate proofs. IDEs don't generate software.
That used to be his response, he just doesn't agree with the way OpenAI is doing it.
I'm not sure this article is a good way to figure out his stance on the issue, I'd recommend reading his blog posts or mastodon threads.
I really think that you should actually read the article.
holy sht, I can solve way harder math problems now. I'll just start on this one over h..."
Aand it's gone.
"Oh wow, that opened the door to a whole new area of..."
Aand it's gone.
How can this possibly be considered a bad thing?
Math culture optimized for thinking skills of proof-based understanding. Funding and education partly determined too. 3blue1brown did an analysis recently.
How can putting effort in and then repeatedly having the rug pulled be considered a good thing?
Every technology revolution needs its John Henry, I guess.
Anyone without a big C in their job title will be on war footing soon enough.
Cobblers
CEO? Circus clowns?
Is there an echo in here?
10/10
Carnival Barkers
So Carpenters are okay but plumbers and electricians are not.
It is easy. We heard many angry programmers going ballistic about (un)maintainability of slop. That's the same, but very much more complex: imagine a large proof that maybe looks correct but it was written by a mentally unstable person that just committed suicide. What is its value?
"looks correct" vs "verified correct by a formal verification language"
Can you help me understand the difference in your analogy?
>The lab agreed to sponsor a workshop at the institute for what Dr. Tao said was $60,000 to $70,000
That's a lot less than i expected. The value he gave back to them should be at least 2 magnitudes higher.
I find it interesting that, several years ago when discussing AI, folks used to focus on how automation would first come for blue collar work. Things like driving being automated and truck drivers replaced. And then eventually on the horizon we would see things like this.
But we still have no self driving cars. Seems like the automation came by in the opposite direction. Perhaps driving will actually be the final thing automated.
> But we still have no self driving cars
While I agree with your statement overall, as someone who drives everyday in LA alongside Waymos without anyone inside of them I must disagree with this aspect of it.
We still have no general self driving cars. What we have is a bunch of geofenced tests. While we are closer than ever, we are still seemingly a long way away from truck drivers being obsolete was foretold over 10 years ago now.
“General” would mean winter driving and I’m not aware of any large-scale tests of things like icy conditions on hills.
Edit: nevermind. https://www.cbc.ca/news/business/waymo-toronto-winter-self-d...
Waymo has been winter driving in Tahoe since 2016 or so. Hard to find icier conditions with bigger hills.
TIL, thanks. That’s heartening to hear as I live in one of those places, or I used to?? The last winter was scary mild.
A better formulation would be: we don't know if we have self-driving cars.
Because if it became fashionable for pedestrians to wear large green dresses with red balls, and everybody would wear that, we have no idea what the AI would do.
It would work fine. seriously what are you on about?
This is a general point rather than an argument supporting the GP comment, but it can be shockingly hard to know what the correct response to particular situations is, or predict how a system will respond. For example, one system I know had difficulty differentiating people laying on the road from unmapped speedbumps (particularly at night), but was very good at recognizing them standing up. Someone spent a lot of time testing with dummies until perception improved. Another had no idea how to handle people in fursuits and halloween costumes, because it was incorrectly applying animal behavioral models to pedestrians.
That's why the latest self-driving systems include reasoning models that draw from the massive amount of knowledge embedded in LLMs. Language evolved to communicate things that are not here and now after all.
Driving is actually regulated.
Something I'm noticing a lot is that automation finds easy footholds in unregulated industries because there's no basis to push back on it. And there's a lot more tolerance for poor quality work in unregulated industries too.
An LLM automating web developers with 99% success rate saves the company millions of dollars and allows them to launch products and features faster.
A truck or a car that has a 99% success rate would be the top threat to society and quickly rise to the leading cause of death under 30 if widely deployed.
Examples?
the point was that 99% rate of success is good enough when failure means nothing, not so much when it means dead people.
So, a treatment that cures cancer 99% of the time but kills the patient 1% of the time is unacceptable?
You have to look at the benefit of something when balancing against a cost.
Consider that the average person interacts with motor vehicles much more often than they would with a potential cure for cancer
And the same argument can apply there as well.
>quickly rise to the leading cause of death under 30 if widely deployed.
Wait, aren't human-driven cars already the leading cause of death under 30?
An LLM automating web developers basically puts the company out of business. Why would customers pay a developer when they can just build it themselves?
There are a lot of things that people are capable of doing themselves that they pay other people to do for them.
I agree that LLMs have and will continue to increase the number of activities that people can DIY. But I believe many people will still choose to pay for others to do things on their behalf.
“99% success” is too vague to be especially meaningful in such different use cases.
99% successful web development where the 1% missing is security that and the company leaks its entire repository of user data every few months is not good.
99% successful car driving where 99% of 5-year periods have zero accidents per car is an order of magnitude safer than the average driver. (And gut feeling, I suspect approaching the tail-end of the safest drivers on the road.)
>99% successful web development where the 1% missing is security that and the company leaks its entire repository of user data every few months is not good.
It feels like it's happening every Thursday and nobody cares. They just give people credit watch coupons or what's it called, and move on with their business. Worst case, a few pennies in fines.
Well 99.99% is you have a major data breach every decade or so, but there are lots of companies, so on aggregate across all of them it's every Thursday.
But if CVS leaks your purchases on a weekly basis, it's probably going to affect people's willingness to shop there. (Or at least to use non-cash.)
I have a self driving Tesla, as do many others.
(Supervised)
Yeah, I'm supervising, and I don't think I've had to take over any time this year.
In 2025 it was occasionally driving weird. Today it's a much better driver than me.
> I don't think I've had to take over any time this year.
That just makes you less prepared when you do have to take over. That's the danger of almost-perfect self driving.
Exactly. Everything below L4 is _incredibly stressful_ and unpleasant to drive, because you have to be constantly aware and alert without having anything to do.
In the case of Tesla, daring to call such a system "Autopilot" is a breathtaking level of irresponsibility. You are responsible for the vehicle you are driving, practically, morally and legally, even if a companies' marketing and the system itself does its very best to divest you from that simple and obvious truth.
In that case, autopilot is the correct term.
Pilots still are required to be able to take over immediately for an autopilot system and are responsible and accountable for all those items you list and more.
Calling it autopilot is precisely what it is, calling it self driving would be false marketing.
That is an absolute _hogwash_ of an explanation, and it comes up every single time this discussion is had.
We are talking about cars, not planes. Driven by regular people, not pilots.
It's a term chosen specifically to evoke a certain connotation among the majority of people, and you know it.
With this line of reasoning I can sell any car as a plane without wings. It flies, but only off a cliff, and doesn't land, but I only said it flies, not that it lands.
Most people expect other things from something marketed as flying, but specialists know that this is exactly how most things fly. And lawyers know to read the fine print.
/s and argumentum ad absurdum, sorry for eristic tricks.
> Everything below L4 is _incredibly stressful_ and unpleasant to drive, because you have to be constantly aware and alert without having anything to do.
Hasn't been my experience for the past year or so, give it a try sometime. Incredibly relaxing and frees up my mind to focus on potential hazards further than just one car length in front of me. Sometimes (don't hate me) frees up my hands/eyes to handle other things that need some temporary attention. Traffic jams, getting cut off by impatient drivers, being stuck behind slow drivers, none of it bothers me. I'm chilling out and talking to my kids and enjoying the scenery.
So basically, you're treating your Tesla as a Level 3 or Level 4 autonomous vehicle, even though its driving system is only Level 2. If you were endangering only yourself, that would be one thing. But you're also endangering other drivers sharing the road.
The "Autopilot" argument is ~5 years old. Teslas no longer have that feature.
The current FSD system has no relation to the old Autopilot, is enormously better, and very pleasant to use. A year ago FSD was nice, but I had to take over occasionally. This year it's much better, and I've yet to see a weakness, aside from some parking issues.
It's definitely a better driver than me!
Self driving in a winter storm? Self driving in torrential rain? Self driving when mud covers a sensor it needs? Self driving if it hits someone? Pretty sure Tesla would say you were driving it then.
Driving is heavily regulated, and there are a million interest groups lining up to sue to stop self-driving. Imagine all the people who make their money from car crashes, for example.
Broadly speaking, this is proof that there will be no jobs coming after AI.
All past inventions have put some of the most miserable humans out of a job. Farming by hand is hard, so is copying books and don't even get me started on the dullness of making clothes by hand.
Driving all day isn't all that far off, though still much better than the above and definitely better than riding horses all day.
Telegraph operators? Hell no. Dude sitting in an elevator all day? No thanks.
It's always been from the other end. This time around, there's gonna be some 10-20 years of robot manufacturing, then a universal lifetime of robots fighting misaligned robots until enough paperclips have been manufactured.
Or you know, we block out the sun and live in caves or whatever you fancy.
The physical world is still more difficult and messy than discrete logic (theorems, software).
> But we still have no self driving cars.
Do you live under a rock?
Uh, they aren’t trustworthy and they aren’t fully autonomous. So no, we indeed do not.
By that standard we don't have human drivers either.
0 self driving cars in my country
There are no elephants in my country, they must not exist.
I see your point but if self driving cars existed, worked like advertised and were economically viable they would and should be in every country in the world.
The same isn't true for elephants.
It seems fairer to say that the Waymo fleet has >4,000 driverless cars [1]. There is still a long way to go, but it's rising.
[1] https://pages.skybrian.com/2026/waymo-robotaxi-fleet/
> folks used to focus on how automation would first come for blue collar work
Developers are guilty of hubris and they are getting slapped back to reality.
Developers are guilty of making reasonable projections based on contemporary industry trends, and they're getting slapped by unexpected revolution in computer science.
Yeah, as always in AI hard things are easy and easy things are hard. How many times have I heard condescending comments from programmers that radiologists are just about to be replaced by AI. And well, AI turned out to get kind of okayish at programming much faster than being acceptable at being radiologist.
The inconvenient truth is the “desk jobs” involving a human operating a computer are far easier to automate than piloting a physical vehicle through a complex environment… A desk job is doesn’t require lidar and cameras…
It was too easy to assume that an AI would never approach human intelligence and hence would only be used for “boring” jobs like driving.
I’ve long disliked the hype around AI but now see that human intelligence is perhaps slightly overrated, at least in terms of the loftier positions seemingly requiring such.
Claude Opus puts to shame any highly caffeinated “10x” software developer. Not saying it’s perfect, but damn good. It can knock out difficult code analysis/reverse engineering more than 20-40x faster than I can. There was even a time long before AI when people thought the same of me…
Hell, at this point, I’d rather deal with Claude than a low-cost offshore team that puts up crappy implementations with endless go-backs and rewrites. I say this from actual experience, not xenophobia. There likely are some high performing offshore teams, I just wasn’t lucky to have the chance of working with one. Have had a couple of local colleagues that were worse… Claude’s probably much cheaper too.
Unfortunately, the “knowledge worker” jobs historically tended to be higher paid.
On one hand, AI is a major asset to experienced professionals with access.
On the other hand, it robs junior engineers hard-fought experience - much like watching a movie instead of reading the book.
And longer term, I think the entire economic structure of society is going to change. Doctors, lawyers, software developers, engineers — none of these are safe from AI reducing the need for headcount.
human intelligence was always overrated, at least in terms of it's actual value to society. phds are often unemployed or "overqualified" for the roles they apply for, roles that pay the most are often roles which are less deskbound and more client-facing, roles that ai cannot replace.
>roles that ai cannot replace
Which role is that, and why you think so ?
alot of investment related roles, those require reading human emotions and pleasing people, a pretty face and pleasant demeanor with emotional intelligence helps more than raw iq.
On one hand, i think investment is no longer fair game. Take a look at what the rich doing in US, blatant inside trading without any consequence.
On other hand, in a completely fair market, i think AI can make profit. A lot of traders just stay at home and monitor news.
Human level embodiment took 10,000x longer to evolve than human level abstract and symbolic information processing, and is also probably 10,000x harder to replicate in an alternative form.
Blue collar is embodied, white collar is abstracted.
It's a well known problem in AI. It's called Moravec's paradox.
https://en.wikipedia.org/wiki/Moravec%27s_paradox
One way to think about this is that the parts of our brain that are responsible for spatial reasoning and the basic automatic stuff we do day to day to just navigate the worlds are evolutionarily the most sophisticated and oldest. Evolution has so taken over this job that most of the time it's automatic and we don't even think about it, which makes it feel easy even though it's wildly complicated when you actually sit down and try to analyze and intellectualize basic stuff like navigating a 3D space in which almost anything can happen.
Intellectual pursuits are, by comparison, relatively new. Part of the reason they might seem so impressive to us is simply because we can't rely as much on eons of biological evolution, so even though what we are doing most of the time is really simple it seems "smart and sophisticated" compared to the far more complex mental operations that we are lucky are just automatic.
Think about it, you have an entire complicated as hell biological interior system that your brain manages continuously without so much as a conscious thought.
This is also why this hubris around the idea that LLMs rival human intelligence is quite laughable. If anything one of the major reasons they are so "great" is because they don't have to deal with a host of issues themselves (their computation is not responsible for keeping their bodies alive and hearts beating 24/7, data center ops takes care of that, unlike our computational system which, in addition to solving all these intellectual problems, also needs to regulate the body continuously)
I think fully automated driving is not so far off. Once the technofascists have their utopia, they will just allow full self-driving vehicles in every road in the country and the people will deal with it regardless of actual capabilities.
There is more than one way to skin a cat.
whte collar work produced more training date these systems trained on...
I am not surprised that this cage rattling of the academy landed on the front page of the NYT during this period of economic and political tumult. Mathematics can, and it should be an open question if it should, exist independently of provenance. I don't see mathematicians speaking with altitude about the economy of provenance; where AI may be dis-incentivizing mathematicians by eroding discovery claims; I see only entitled affront. But perhaps, if they are being honest, the glory of discovery is viewed as a critical motivator. If so, mathematics is thus imperiled by human vanity, not AI. The same logic applies to thinking and grappling with proofs -- it is a human choice to turn off your thinking. AI is attributed with false agency here.
I don't know if this will happen in math, but in other fields where computers have outstripped humans (chess and poker, for instance), there's been a loss of creativity, but there have also been other forms of creativity that take its place. There was a period of reeling where we had to figure out what it meant to just be able to know answers to the question that made the game fun, but there's also a moment of realization: just because a computer says something doesn't mean we can't make it our own. Using poker solvers to find creative non-equilibrium strategies can still be fun: the ingenuity comes from using the tools to think out side the box. Or, finding a nicer set of abstractions that explains why a strategy does a certain thing, and then starting to notice it showing up other places.
For math, just because we know a thing is "TRUE" doesn't mean the investigation is done. The folks that love math are driven by solving puzzles, and the puzzle is still there, only changed: instead of being "is this true?", the puzzle is now "why is this true?" Building theories, finding nicer proofs, etc: there is still plenty of room for creativity.
But in the meantime, it really is tragic that so many young minds have had their work stripped away from them.
Chess and poker as spectator sports have a high incentive to see humans compete fairly, and I think that's the reason why there are such strong anti-cheating measures (at least in chess; in poker, too, I suppose).
And the economy puts no such large incentives on much of the remainder of economically valuable work being purely human, quite the opposite actually. And instead of regulating the AI industry (which produces the "cheating tools"), they get trillions of investment. So this seems to be going in the opposite direction where it is actively worked against humans staying economically relevant.
I know he says he’s ant talk a human about the proof, but why can’t he talk to ChatGPT?
Is the cost prohibitive , or a proprietary model?
Same as code, the llm can generate vast amounts and it seems to work, but no one understands the documentation Claude Code, or other LLMs, produce. Essentially, garbage because, to make use of it you need to be able to understand it, usually at a cost (unquantified), and if only LLMs do then what is the point?
> if only LLMs do then what is the point?
It turns out it doesn't matter, because outside of a few narrow bands like Claude Code, no one cares what documentation an LLM writes for your project, because no one is ever going to go looking for someone else's project or library to solve their problem anymore.
So either an LLM decides to pull in your project as a library for reasons, in which the LLM can understand the documentation, or else no one besides the creator is using it anyway. So it doesn't matter.
Why would anyone use someone else's AI-coded project if they can get their own version that better fits their own needs in less time?
Sure you can make Claude produce documentation & code that is readable. You need to steer it and show it how you want it to write. When it gets it wrong, find counter examples so it can learn the style you want. Otherwise it's going to write what it thinks is best. What is best for LLM comprehension and efficiency is not necessarily best for the human.
It's interesting to see this all play out. Yes, on a personal level, it's a bummer for mathematicians that have the goal of figuring something out, and getting personal recognition and prize money. But now that AI can do this work better, I think we should mostly just celebrate that we can suddenly solve a lot of problems, and figure out how to use these abilities in a productive way. Math needs to change, just like software development has massively changed.
Both can be true.
Real grief for mathematicians, coders, artists etc (not waved away as "he is just in stage 2 bla bla").
But also: yes of course, the challenge now is to use these supposed super powers for good.
I imagine this is what farriers felt when the automobile came out.
This is the language of someone who is blind to the reality of actual war. I’m sorry, you don’t have PTSD because computers got good at theoretical math problems, and part of the reason half our population looks down on elites is they talk like this to each people who got hit by an IED in Fallujah.
I do believe after the initial shock mathematicians will be able to use their math knowledge to solve practical problems, instead of lets solve this conjecture, prove this age old math riddle, how the pattern is possible. They may have some uses in fringe areas, but it doesn't seem all that useful. These guys are obvious quite brilliant, so when they combine it with other fields which they can branch to due to LLM's, they can still stay relevant. Ask your software engineer how that went.
IMO the most useful thing a mathematician can do is not solve “practical problems” but to come up with conjectures and riddles that look around several dark corners of math at once. The proving of a conjecture is a bit of a sport done to impress people with your cleverness; but the clever person was the one who made the conjecture to begin with.
Given the trajectory of LLMs to date I see them helping construct proofs for conjectures but not devising new conjectures of any material substance any time soon. The challenge is, as Tao has said elsewhere, part of being able to formulate a conjecture is by exploring the landscape around it by doing proof research. Seeking answers finds useful questions. The fear is the tools will take away the exploration of the landscape. But that’s silly IMO. It takes a special type of lazy to let a tool take away your understanding that’s important for what you’re goal is, and a special type of passion to learn with a powerful tool. The passionate will adapt and progress will accelerate, not slow down.
For instance Tao has posted some of his interrogations of proofs with AI assisted reasoning and it didn’t seem to diminish his ability to establish insight rapidly, but to shut down avenues rapidly and to pivot and expand his understanding rapidly. The insight was all his own, as was the path of inquiry. The understanding of the output was his as well. He carries it into tomorrow and uses it to formulate new more interesting conjectures the next day. The AI ceased to “exist” as soon as the inference turn was over.
The hand wringing is pointless and lame. John Henry moves aren’t necessary or useful, and when I see a tunnel boring project now I see tons of people well employed there, just the holes are bigger and better, and they’re engineers instead of strong backed hammer slingers.
Mathematicians might just be experiencing the first phases of the cycle of acceptance - resistance and anger, next is depression then eventually embracing it. Software developers as a whole are a bit further along the cycle.
"just". I think you should "justify" your use of "just".
Because it comes across as "ooh, you're just going through the five stages of grief, dummy! Look I've taught you psychology 101. Now that you know about grief, you might as well skip to the next cycle already. Support me on Patreon. Like, comment, subscribe"
Pointing out that someone is "just" grieving is not helpful.
I'm seeing this a lot in the past months of AI-for-math discussions. Had to get this off my chest.
I hear you.
Yeah, after I posted that I wondered whether someone would just focus on that word. You didn't just do that though, you went scorched earth - I meant no offense and sympathize with everyone affected by changes, I'm a developer and learning to embrace the change after a strong bout of existential crisis.
Math isn't useless. One of its defining features is its "unreasonable effectiveness" in formulating scientific ideas. It's hard to say exactly why it's so useful, but it is, even if mathematicians aren't trying to make it useful.
It's not at all clear whether the kind of math created by LLMs will retain the usefulness of the old math. LLMs are good at rigor but bad at intuition. It's not even really clear if the rigor was ever all that important. Theoretical physics is full of people using math in ways that don't meet the bar of rigor that mathematicians set for themselves, but they have enough physical intuition for what they're doing, so it doesn't matter. It's an open question whether post-LLM math will continue to supply scientists with the kinds of ideas that they need from it.
I keep waiting to hear that some LLM has produced a fully rigorous quantum field theory
I find this entirely self serving.
Terrence Tao was very supportive of AI and formalizing math with lean when it looked like it was giving ‘generalists’ like him an edge over mathematicians too deep into one particular niche field.
But now that it’s letting everyone, including mathematicians who are perhaps too specialized, explore ideas and patterns from related math fields, he’s suddenly ‘on a war footing’.
I think it's a bit of an unfair characterization, see this post for the nuances in how the math community approached the development:
https://news.ycombinator.com/item?id=50128468
entirely fair.
basically both sides now dislike that he flip flopped
its either you are anti-AI all the way or flexible and adaptive without making strong opinions that can be put on record.
most people are in the latter and its growing. math is solved.
> basically both sides now dislike that he flip flopped
No, the dumb thing is the idea that there are "sides".
> basically both sides now dislike that he flip flopped
Literally the only people with this opinion of Tao are internet forum warriors who have no expertise in the field and who's opinion of Tao don't matter in the slightest.
> who's opinion of Tao don't matter in the slightest.
Similarly, Tao being ‘on the warpath’ does not matter in the slightest when it comes to formalizing math and finding proofs to important unsolved problems with AI.
> Similarly, Tao being ‘on the warpath’
Do you think that this is a quote from the article you just read?
I swear half the comments here are just from people reading dunks on r/singularity and x and getting real mad at strawmen.
“I’m on a war footing,” he said while grabbing coffee during a two-day math workshop at the University of California, Los Angeles, that was rife with talk about the existential crisis that artificial intelligence has created in his field.
> “I’m on a war footing,” he said
So not remotely the same thing.
> Literally the only people with this opinion of Tao are internet forum warriors
I find it amusing that you would be the one saying it here.
> But now that it’s letting everyone
Eh... That “everyone” is a multi billion (trillion?) $ company paying top mathematicians specifically hired for generating math proofs.
No, pretty much every math PhD student and researcher is now using the AI+lean combo.
So as every high schooler. That doesn’t mean much for actual results similar to what OpenAI “generated”, and doesn’t quite explain the “war footing”, does it?
We’ve yet to see the democratizing fantasies in math field to materialize.
Which makes complaints by mathematicians about it absurd. They should just stop flapping their lips; there is no putting the genie back in the bottle.
Why so much resentment? To be a mathematician (I’m not one), you need to be relatively smart, hard working and passionate, considering it doesn’t usually pay well. These are admirable and aspirational.
If mathematicians were saying "the modern economy smashes the average person, and now we're in the same boat", I wouldn't be negative about them. But they aren't saying that. They're saying "our position of relative privilege is threatened and we must defend it."
> relative privilege
What privilege? Did you miss the part where it doesn’t pay well?
Funnily enough, the understanding of modern economy is achieved through mathematics, developed by mathematicians and economists (using tools provided in math)
> They're saying "our position of relative privilege is threatened and we must defend it."
No, they are not.
I don't think it is self-serving. Tao has stated plainly that he thought LLMs would go the route of assistants, like co-pilots. But what he feels now is that they are actually being engineered to be replacements. His claim is that the way OpenAI dropped these math results isn't "assisting" anyone, so we should all read between the lines.
Consider any man at his job, fighting the good fight. Your boss says "I've hired this man to assist you" and you are happy to finally have some help with your difficult task. Then one morning you come into work and see that the coming day’s work was done overnight by this other fellow. And the realization sinks in, he isn't there to help you, he is there to replace you.
In this view his reaction seems totally expected. I expect many professionals, e.g. doctors, lawyers, accountants, etc. will make this realization sooner or later. The companies are saying these tools will assist professionals, but in reality they are aiming to replace them.
> But what he feels now is that they are actually being engineered to be replacements
lol. lmao even.
I guess there is a first time for everything.
"doctors, lawyers, accountants, "
Regulated fields - another clueless poster lol.
I know many of you really hate whats happening but don't try and project it on other professions where the environment is different.
Society largely never cared about maths.
you may not be aware of it but society largely runs on the results of maths, clueless indeed. and regulated or not, if there are financial savings to be made anyone can be shoved under the bus.
You might be mistaking my comment as a value judgement rather than an attempt to charitably explain the latest media communications from Tao. I detect in his position that some trust he granted the AI companies has been violated.
You are, of course, right that doctors, lawyers and accountants have more control over the environment they work in compared to mathematicians. But it doesn't change the underlying argument Tao is making. Your observation that those professions will react differently is likely to be true and only time will tell how effective their response will be.
But AI "assistants" is a marketing approach being made to all professionals at this time. Tao is implying this is a Trojan-horse strategy. If you let the assistants in without reasonable protections, you may lose control over the environment you are trying to protect.
> Regulated fields - another clueless poster lol
Out of sheer, idle curiosity: were you actually laughing when you typed that out?
> The companies are saying these tools will assist professionals, but in reality they are aiming to replace them.
If anyone doubts this, consider that Anthropic considers its TAM to exceed $30 trillion which is nearly the entire GDP of the US and 25% of the world GDP.
Only makes sense if they believe they will massively replace labor. Which, to their credit, they used to admit openly and publicly and only stopped because some crisis PR people told them "hey maybe you shouldn't say the quiet part out loud while the hoi polloi still have the power to stop this from happening".
You do realise Anthropic's management, after throwing its tantrums, gets a seeing to and has to do what its investors want? Which is pump up the valuation.
You're not this naive are you?
Amazing, truly.
Do their own hiring practices reflect that ambition? They sure seem to be recruiting a lot of humans for typical roles in business, legal, and engineering. If they want to flex the power of their models to automate human jobs, why not lead by example?
https://www.anthropic.com/careers/jobs
> They sure seem to be recruiting a lot of humans for typical roles in business, legal, and engineering.
They have practically infinite investor money to throw at salaries (lost in the noise of how much they are spending on compute) so why not use it for now to reach their goal as fast as possible?
My thesis isn't that they have already achieved the ability to replace massive amounts of the labor pool, just that that has to be their goal given their stated TAM.
> If they want to flex the power of their models to automate human jobs, why not lead by example?
They don't want to flex this. They realized (after a false start) that it is better for them to avoid talking about this in public.
That doesn't mean their goals changed, they just realized that flexing before the goal is achieved could endanger the goal being achieved through political backlash.
>They have practically infinite investor money to throw at salaries (lost in the noise of how much they are spending on compute) so why not use it for now to reach their goal as fast as possible?
Wouldn't throwing that money into GPU be better because AI is smarter and faster ? So they would reach their goal even faster ?
I’m not making a claim one way or the other about the intent of these companies, but if your product made labor 3x more productive, you could still easily justify a TAM of the entirety of US GDP, without resulting in anyone losing their jobs. Obviously, here in reality, AI does act as a near 1:1 replacement for people in some roles, so we should expect some job losses. But I don’t think there’s any reason we should expect the entire US labor force to be automated away any time soon, even taking these assessments at face value
>Tao has stated plainly that he thought LLMs would go the route of assistants, like co-pilots.
As one of the smartest people in the world, he is so naive to believe that those capitalists will stop at that.
Tenured at age 24, I doubt he has any experience in industry to understand what he was getting into. Which makes me even more incredulous as to why people worship him.
The reason we fell first is because we embraced the copilots. We used them heavily, this gave them more and more training data on top of the code they slurped up from our using their assistants. Soon the assistant became the agent who killed the human.
They also had a rich starting point from open source code (which we somehow gave up without realising it). All of this won't happen as efficiently for these other fields, but it will happen, much in the way you've described. We (swes) turned out to be a rather dumb group of people, which is hilarious since we think we're clever.
The only moat we have is the human to human element, we need to talk to other humans in the business. Customers, etc. But once they're replaced by machines or automation, then machine to machine communication will be the preferred mode of communication and work and the legacy humans will be increasingly cut out of the loop. Human in the loop is a death sentence we just don't realise it.
Isnt OpenAI and specifically Altman openly talking about that being the goal?
> The companies are saying these tools will assist professionals, but in reality they are aiming to replace them.
They are openly saying that the goal is to replace humans and make humans obsolete. Like, literally openly. I am not saying I agree with that goal or find it realistic, but they do think so.
A few-minute search on Google shows that Altman has said a lot of contradictory things on the subject. A few quotes, as examples:
“AI won't replace humans. But humans who use AI will replace those who don't.”
vs
"Some areas in the job market will be 'just like totally, totally gone' as they're replaced by AI agents.”
and
“AI will probably replace most of the jobs people do today,”
The most recent position I could find says he has revised his earlier position on a total replacement due to the lagging adoption of AI in many industries. But I don't think there is a single position we can point to that they are "openly saying". It is fair to grant even the CEOs of these companies a change in position as they gain more information about capabilities and adoption, rather than insist that they hold, have held and will continue to hold fixed opinions.
The point is that Tao's understanding has changed. He may have been naive before, he may have heard in their words something he wanted to believe. Perhaps he was misled by people who he trusted that worked in the company. But now that he has more evidence, in the form of the maths drops and the way they have been handled, his suspension of disbelief no longer holds. The companies could have done this in a way that included mathematicians, so they chose not to. And that choice reveals their aims unambiguously in a way that a media-trained CEO or careful PR department can avoid.
That suggests that Tao is not being "self-serving" as others claim. He is saying that his optimism in the best-case scenario turned out to be incorrect.
I've never perceived him as 100% supportive. He has rather been open-minded about a new technology and exploring what it can do. Now it turns out it can destroy his field, so he's naturally against it (at least against the destruction, not necessarily against the technology)
I think ‘destroy his field’ is ‘destroy his method of being famous in the field’.
Terrence Tao is famous because of solving problems better that most mathematicians because he has an uncanny ability to look across different math fields. AI gets everyone this ability for 20 to 200$ per month, eventually free.
Most mathematicians are happy to see interesting problems in their field being solved, and are looking to build on these to find more interesting problems.
Hm... I'm not a mathematician, but why would these new more interesting problems not be solvable in the same way by the same - or newer - models?
They will be, that’s the point.
The point is to make the field progress by discovering new things!
Who gets credit for what and how credibility is assigned is going to be muddy for a while but that’s the case whenever a bunch of new science happens in close sequence. History is full of math/science discoveries having debated and dubious provenance.
I can't see how the field can even exist - not to say progress - if any problem can be solved before a human can understand it. Looks like mathematics without mathematicians, "progressing" in the same way as paperclip optimizer progresses in its productivity.
Math doesn’t exist to make mathematicians famous.
It provides deep insights into logic, computation, provides tools for us to understand the universe, establishes mind blowing relationships between seemingly unrelated things.
For example “how much information can a black hole contain?”
> provides deep insights
To whom? If there are no humans in the field, there is no one to get the insight. Maybe you are right, and there is just a new type of a mathematician being born, but as an outsider I just can't see what they could look like, what will be left for humans to contribute
There is a huge jump from
AI solves math problems to
> If there are no humans in the field
Realistically, math will be done by well funded teams of people instead of cult of personality mathematicians.
Also, insights from scientific discoveries are for everyone. You do not have to understand the complex multi dimensional algebraic geometry of general relativity to appreciate that gravity bends time as well as space. You don't need to understand fifty years of linear programming research to use a modern solver.
> Realistically, math will be done by well funded teams of people instead of cult of personality mathematicians.
Most math is already being done by meagrely funded mathematicians. The entire US federal budget for mathematics is like $100M. One college football coach can already make 10 percent of that. No mathematician is making bank.
Is the implication of all this that mathematics research should get a cash injection to pay for high-powered computational tools?
> Is the implication of all this that mathematics research should get a cash injection to pay for high-powered computational tools?
Math will, sure. Mathematicians, doubtful. After all, most high end physics research with billions in funding is now done by postdocs making a lower middle class salary.
It remains to be seen if "any problem can be solved before a human can understand it". What if it turns out there are (many) problems too hard for both AI and humans.
It has been proved a hundred years ago that some problems can not be proven. So there are problems AI will not solve.
Show me the mathematicians ecstatic about OpenAIs recent results.
One might say, in the end, what's wrong with being self-serving? Are we _all_ meant to be self-sacrificing? Are we all meant to be the eggs that get cracked to build this wonderful future ommlette?
Fine. I will self-servingly dismiss his concerns. They don't concern the important people here: me, myself, and I.
To bend a phrase, if you have to ask...
What did Niemöller say again? First they came for...
TLDR: "I didn't understand this proof and there is no one to explain it to me"
The TLDR seems perhaps tongue-in-cheek, but it's a worthy thought: the situation where our best experts find new science to be inscrutable is close at hand, if not here now.
Humans have been guilty of burying things we don't understand for millenia. Will we continue to do so "because AI"?
Inscrutable through lack of effort communicating (OpenAI) is different from inscrutable because it’s high level hard to understand (Grothendieck).
For me it just shows that modern math is not that important and mostly ego driven. If it was important, mathematicians would cherish the progress. I can't imagine bio researchers get mad that AI cured cancer.
Maybe partially.
I think this sort of progress, compounded over the next N years will serve to cleanly split useful math from the ego driven math you speak of.
Certainly there are enormously impactful pure math results yet to be found, but we have no idea really which directions to pursue.
I wonder if this is going to look like the chemistry-alchemy split in the rear view mirror.
It was devastating to learn in my late 20s that 99.9999% of what the average person does is based on personal ego and not a communal vision of the future.
There are plenty people in every discipline that prioritize their ego over measurable progress towards a stated goal - even less so a community focused goal.
Its just the modern day version of the stuff they told in the religion hey-days.
Humans aren't that original. We just reinvent stuff we used to do to suit the present day, with our own twist.
Pure Mathematics is closer to philosophy or art than it is to empirical science.
In Pure maths, people are not generally solving problems because of some pressing practical need, it's purely out of intellectual interest, and if we're lucky there's some immediate practical application. More often, the knowledge sits in pure form for a while and years down the road some new invention, or practical consideration, or other field finds a useful application.
Just like literature and visual art, it serves an important epistemic and social function even in spite of its immediate lack of raw practicality.
You are very wrong about bio researchers! I am a mathematician who has worked in bioinformatics and, just like we're seeing with a few curiously well-placed-to-obstruct-progress mathematicians, are in it for power, influence, and credit and anything that erodes any of that is bad, bad, BAD!!!
> They “used math for what they needed, which was to evaluate their models,”
OAI first paper on the prize was a pretty shitty thing to do. But the rest of this looks like they are just mining the corpus and taking a brute force approach to do it.
Im going to say this again, the "pure math" academic types need to get a grip. Plenty of your peers got PHD's and happily made a fortune in finance, while screwing the world (See 2008 housing bubble) and none of you said a peep about that.
Plenty of welders made weaponry that killed babies and none of the famous DIY Youtubers spoke out against that either.
> Im going to say this again, the "pure math" academic types need to get a grip. Plenty of your peers got PHD's and happily made a fortune in finance, while screwing the world (See 2008 housing bubble) and none of you said a peep about that.
They call it the most populist post of all time.
I wish Terry the best.
Wow really? I didn't know all pure mathematicians were elitists
You are right, we should get rid of their profession
I would usually have been part of the downvoting brigade for this comment.
But to be honest the reaction from the ivory tower here is seemingly quite telling to a layman watching from afar.
It looks far more like this was some extremely gatekept community where you were only allowed to work on sanctioned things if so deemed worthy. Better not step one someone’s toes lest you get exiled! How much progress was lost due to newcomers never working on a problem due to told not to?
It’s starting to make those old timey Usenet kooks look a whole lot less crazy to me. They seemingly were right about this part.
Mathematics was funded and supported by a whole bunch of janitors and blue collar workers busting their asses to let entire departments of thinking men and women work on hard problems for the betterment of society. If it was just a super special friends club the whole time that was gatekeeping what amounts to a hobby, it’s going to me much harder to justify such a social contract.
Honestly not even sure what to think at this point. Extremely disappointing to me the more I read from these people.
I hope the LLM's will tackle theoretical physics next. If you think the math community is bad in terms of gatekeeping, and it is, the physics community is so much worse. Even community insiders are afraid to share their more unusual ideas at risk of becoming pariah's, outsiders have no chance. And that while they seem more or less stuck in their current track.
Admittedly it's also just really hard to come up with something better than the current track, but doing better has to start with being eager to explore different directions. Even if the new directions don't quite work just yet. And that eagerness just isn't there in the community, new directions are threats to the careers of sensitive people
Theoretical physics would, from my outsider view nowadays, benefit from an injection of vitality and an ability to tackle new venues. But the question is open whether LLMs can truly break new ground or if they work within the convex hull of current theory. And if that matters, too.
"Ivory tower" complains about people in low power scientific positions by people the most advantageous industry existing are ridiculous.
What are you even talking about here? Mathematics was funded by janitors?
>Mathematics was funded by janitors?
How do you like them apples?
In the past there was too much activation energy to point out flaws in other’s reasoning. This is a natural response to slop cannons even prellms with misinformation shared.
Is Terence Tao just another AI booster nowadays, by the sheer amount of PR generating posts? Reading HN one might think that there is only a single mathematician in the world left.
Case in point: https://hn.algolia.com/?dateRange=all&page=0&prefix=true&que...
> Is Terence Tao just another AI booster nowadays
The information in the article suggests that he regrets his prior hyping of AI.
I remember just last year he said the LLM were like incompetent assistants, but not completely useless. The tech advances are mind boggling just looking back at that.
OT but what is is that has enabled these advances? Bigger models, better training, more compute, reasoning, all of these?
He'll eventually get to the acceptance stage for the loss of what was.