The error was saying that "infinitely many alphabets can be generated" but there is a finite number of parameters which have a finite range of values. If Knuth had just written "a humongous number of alphabets" he would be correct.
Sure. For practical purposes, the number is infinite. This is why I found the bug and the bug report so amusing: In "normal" language, the sentence is correct, but for a mathematician, especially such a renowned professor, it is an amazing blunder. Bonus points for being the first word in the document.
When I was making my presentation at TUG 2019 he suggested _dart_ as a term for a shape of "two straight edges, one concave arc" which then freed up _arrowhead_ for "two convex, one concave arc".
It was a bit more than 25 years ago for me, check #790 for $2.88 DT 33, (143).
Really need to find another error or point of improvement so as to get the digital account --- I've been reading through TAoCP Vol. 4 Fascicle 7 on _Constraint Satisfaction_, but it's been slow going (though I did find out that it is intentional that he not list beginning of chapter quotes in the index).
I wondered how you received a real check since Knuth has not been sending out real checks (as you have noted) for some time now, only to see that you explained it in the very first sentence and I had read over it, just like many people read over the error that you found in the first sentence of the book. Nice one! I wonder what the "Infinitely" was replaced with - probably not "Finitely" :)
It kills me that I was rebuffed when I asked for copyright permission to reprint the Tolkien text _The Old English Exodus_ on the grounds that I was a "Tolkien Nut" and not an academic, then, then I bought a boxed set (which contained 4 other books which I already owned), reading the book revealed 20 typos in the 22 pages comprised of the Select Bibliography and poem (they really should've just used a scan of those twain as was done in other similar texts).
Similarly, it's hard to take current discussion of _Dune_ seriously when the word "pogrom" is set as "program" in the e-book (and yes, I have reported this as a typo, and no, it hasn't been fixed, even though the publisher did "update" the book to change the cover).
I have also found that there are a lot more errors in books published post 1990, then pre. Specifically, in the 1940-1988 period, and more specifically, in the decade from 70 to 80, the quality of books was at its acme. Errors were far less than what we see now.
Tolkien was a memorable read. I read it when I was experiencing Covid-caused depression in 2021.
and as implied in that link, have been reading his work since I was quite young, and dipped into the scholarship and linguistic angle when I picked up the paperback edition of _A Tolkien Compass_ in the early 80s.
I am now on a Trollope binge. That man distilled all of his hard life experiences as musings interspersed between the social dilemmas his characters were facing.
Recommend you start with either the "Eustace Diamonds" or "The small house at Allington".
_Tolkien's Modern Reading_ has the following on Trollope which seems pertinent:
"His (JRRT's) appreciation of (realistic fiction) is underscored by his knowledge of that keen-eyed observer of contemporaneous political and ecclesiastical culture, Anthony Trollope."
I am currently trying to patch up my rather spotty education by listening to books on Librivox, trying for chronological order, so as to build a solid foundation and understanding thereby.
He is quite methodical and meticulous --- I doubt that there is much in the training data which isn't already accounted for in his research for his writings.
I only managed to get one check (for an error and a point of improvement) for _very_ minor points in _Digital Typography_ which was facilitated by my having been fascinated by typography since reading Oscar Ogg's _The 26 Letters_ and his cousin Warren Chappell's _The Living Alphabet_ when I was 8 or so.
They definitely have; lots of the recent bug reports [0] explicitly acknowledge AI assistance. You can also look at the list of pending bug reports [1] and see how many are from 2026 compared to other years (and it takes many months to get the bug reports enough to add them to this list, so this significantly undercounts things).
I also got one for catching DEK out for claiming "Alan Turing broke the Enigma".
That claim goes to the Polish cryptoanalyst Marian Rejewski instead, of course (https://en.wikipedia.org/wiki/Marian_Rejewski); what Alan Turing and Tommy Flowers did was automate the breaking, which was important because it had to be done again every day (due to the many combinations of configurations of the Enigma).
Bjarne Stroustrup did, at some point at least. I have a $32 real check from him for finding an error in "The C++ Programming Language (Special Edition)".
Sadly I think this is the end of an era. Someone should probably run an AI fact checker on this and send him the rest of any errors. Or he could change the nature or requirement of the reward, if somehow it can be proved the error could not have been found without a human's effort.
I wonder if someone has used an LLM yet to analyze Knuth’s books and find errors to inundate him with? Please don’t do that (although I’m sure it’s possible).
> "These account balances reflect only the rewards for errors reported since the beginning of 2006. Many reward checks were issued during 1968--2005, too numerous to mention here."
There's 20 years on that chart vs 37 not on it.
Also that's "account balance" rather than "the most Reward checks" which I take to mean "the most [number of] reward checks" -- there's probably a correlation, yes, but [0] shows a variety of ways where check values are non-constant.
There is only one person that can rule that out, but since this is their statement on the subject I would take it as authoritative unless there is a better source.
You probably have a substantial subset of the people on that list on HN, so it might be possible to recover a chunk of the 'paper era'.
> I would take it as authoritative unless there is a better source.
I'm not doubting the authority on the balances; it's the correlation to the number of checks I'm querying - high balance doesn't necessarily mean high number of checks, especially since the checks can have different values.
I doubt even Knuth has those records, so this is as good as it gets until someone sets off to compile a list of the 'paper past' that has enough proof to back the numbers.
Udo's knowledge of TeX is absolutely stunning, so I would be very surprised if he weren't in first place. And DRF [0] [1] seemed to agree with the ranking in a sibling comment [2], which is also suggests that it's accurate.
> There's 20 years on that chart vs 37 not on it.
The reward values have increased exponentially over the years (I think?), so the older years should be relatively insignificant to the overall balances.
Well, I'm #4, but it's all from TeX stuff (where I'm kind of a ringer), and not The Art Of Computer Programming. The beyond-amazing Udo Wermuth is also all TeX, I believe, and did it without having a home team advantage; everyone else high on the list looks to be strictly TAOCP.
Heh, and I thought I was being pedantic with my reward cheque. In my case I found inconsistent hyphenation in a technical term used in the book. I had wondered how to hyphenate it in my own writing so turned to Knuth to see what he did and was surprised to find it inconsistent even within a single volume of TAOCP! He wrote back with a funny message and a cheque for the back of San Serrif. It's on my wall now.
Just FYI for HN - if there is anyone looking to make big money in the coming years there are no fully signed TAOCP first editions anywhere. You would honestly print so much money if you could get all the first edition volumes signed.
He is incredibly generous with his signings --- even doing one on the spur of the moment in his home when one of the presenters mentioned that he'd been unable to source a copy of _Mathematical Fun and Games_ (I had a copy I'd planned on getting signed, but instead passed it to his wife and insisted that she get a photo of DEK signing it for her husband and that they keep it).
Interesting. I wonder if there is a way to get the completed volumes signed by him prior to shipping all the way to Australia. I was all over abesbooks looking for signed copies but couldn't find anything.
The thing is, the first editions were a _long_ while ago --- not sure how many are in good condition and for sale even unsigned.
Apparently some folks actually paid in advance for the full set leatherbound --- it'll be interesting to see the posts about Vol. 4 being delivered....
True AGI will arrive when an LLM will be able to provide ALL remaining mistakes in Donald Knuth's books. And kill one more amazing thing in the process.
The biggest shame of my life is that I had one of these and somehow managed to lose it.
If that's your biggest shame then you must have lived a good life.
Or perhaps a life not lived
This comment may trigger life changing reflection in hundreds or thousands of souls...
I guess only if you value shame? Which is not a given. HN has so many “shameless plug” comments - HN readers for sure qualify as shameless.
Receiving a Knuth reward check is surely enough to make a life "lived".
but losing that check is like a living death!
I lost one of mine but Knuth kindly sent me a replacement.
Have you checked every page of every volume of TAOCP?
The error was saying that "infinitely many alphabets can be generated" but there is a finite number of parameters which have a finite range of values. If Knuth had just written "a humongous number of alphabets" he would be correct.
If I am reading this right, you can generate 268 435 456 ^ 62 alphabets.
I would say he could have even gotten away with “functionally infinite number of alphabets”.
Some of the parameters are bools. So somewhere between 2^62 and your figure...
Why would anybody need more than `268 435 456 ^ 62` KB of RAM?
Sure. For practical purposes, the number is infinite. This is why I found the bug and the bug report so amusing: In "normal" language, the sentence is correct, but for a mathematician, especially such a renowned professor, it is an amazing blunder. Bonus points for being the first word in the document.
It's not a reward check, but Knuth read one of my articles and emailed me about it [0], which I found pretty cool.
[0]: https://tug.org/TUGboat/tb43-3/tb135chernoff-lwc.pdf
When I was making my presentation at TUG 2019 he suggested _dart_ as a term for a shape of "two straight edges, one concave arc" which then freed up _arrowhead_ for "two convex, one concave arc".
> my presentation at TUG 2019
You missed out on a great time at TUG26 [0], but hopefully I'll see you at TUG27 [1] in Paris :).
[0]: https://tug.org/tug2026/
[1]: https://tug.org/tug2027/
I'm still a bit miffed that TUG2020 was cancelled, and am still waiting for it to come back to the East Coast of the U.S.
It was a bit more than 25 years ago for me, check #790 for $2.88 DT 33, (143).
Really need to find another error or point of improvement so as to get the digital account --- I've been reading through TAoCP Vol. 4 Fascicle 7 on _Constraint Satisfaction_, but it's been slow going (though I did find out that it is intentional that he not list beginning of chapter quotes in the index).
I wondered how you received a real check since Knuth has not been sending out real checks (as you have noted) for some time now, only to see that you explained it in the very first sentence and I had read over it, just like many people read over the error that you found in the first sentence of the book. Nice one! I wonder what the "Infinitely" was replaced with - probably not "Finitely" :)
I had received a check recently and wrote about it too https://news.ycombinator.com/item?id=49286258
The current wording (per Amazon's sample of the 2021 edition) is "Zillions of alphabets can be generated by the programs in this book."
Wait, that doesn't sound right either.
What a brilliant teaching technique, think of how many people studied his work for bounties that they would never cash.
I’m on the mailing list where errors related to TeX are submitted and the level of scrutiny behind submissions is truly mind-boggling.
Honestly, I wish all software were subject to that much scrutiny.
All tech books too!
SFAIK, only Findlay/Watt duo have offered such a guarantee of correctness.
Make that all books.
It kills me that I was rebuffed when I asked for copyright permission to reprint the Tolkien text _The Old English Exodus_ on the grounds that I was a "Tolkien Nut" and not an academic, then, then I bought a boxed set (which contained 4 other books which I already owned), reading the book revealed 20 typos in the 22 pages comprised of the Select Bibliography and poem (they really should've just used a scan of those twain as was done in other similar texts).
Similarly, it's hard to take current discussion of _Dune_ seriously when the word "pogrom" is set as "program" in the e-book (and yes, I have reported this as a typo, and no, it hasn't been fixed, even though the publisher did "update" the book to change the cover).
I have also found that there are a lot more errors in books published post 1990, then pre. Specifically, in the 1940-1988 period, and more specifically, in the decade from 70 to 80, the quality of books was at its acme. Errors were far less than what we see now.
Tolkien was a memorable read. I read it when I was experiencing Covid-caused depression in 2021.
It kills me that the typos in ebooks at least don't get fixed....
It's interesting how different folks approach his oeuvre --- I have a fairly extensive collection:
https://www.reddit.com/r/tolkienbooks/comments/1oa01zr/four_...
and as implied in that link, have been reading his work since I was quite young, and dipped into the scholarship and linguistic angle when I picked up the paperback edition of _A Tolkien Compass_ in the early 80s.
Impressive. Thanks for the link.
I am now on a Trollope binge. That man distilled all of his hard life experiences as musings interspersed between the social dilemmas his characters were facing.
Recommend you start with either the "Eustace Diamonds" or "The small house at Allington".
Thanks! My pleasure!
_Tolkien's Modern Reading_ has the following on Trollope which seems pertinent:
"His (JRRT's) appreciation of (realistic fiction) is underscored by his knowledge of that keen-eyed observer of contemporaneous political and ecclesiastical culture, Anthony Trollope."
I am currently trying to patch up my rather spotty education by listening to books on Librivox, trying for chronological order, so as to build a solid foundation and understanding thereby.
I'm surprised we haven't heard of anyone running an AI on Donald Knuth's books to generate the largest collection of checks in existence...
He is quite methodical and meticulous --- I doubt that there is much in the training data which isn't already accounted for in his research for his writings.
I only managed to get one check (for an error and a point of improvement) for _very_ minor points in _Digital Typography_ which was facilitated by my having been fascinated by typography since reading Oscar Ogg's _The 26 Letters_ and his cousin Warren Chappell's _The Living Alphabet_ when I was 8 or so.
The next headline will read: "AI pilled vibecoders bankrupt a once prominent computer scientist, the figure will surprise you!"
They definitely have; lots of the recent bug reports [0] explicitly acknowledge AI assistance. You can also look at the list of pending bug reports [1] and see how many are from 2026 compared to other years (and it takes many months to get the bug reports enough to add them to this list, so this significantly undercounts things).
[0]: https://tug.org/pipermail/tex-k/
[1]: https://tug.org/texmfbug/newbug.html
Awesome! I know the feeling, I have two myself. https://x.com/loginn/status/1367475093719416833
(Hmm maybe I should also write a blogpost about this)
I bet the mailing cost was more than 0x$2.00 for Knuth.
I also got one for catching DEK out for claiming "Alan Turing broke the Enigma".
That claim goes to the Polish cryptoanalyst Marian Rejewski instead, of course (https://en.wikipedia.org/wiki/Marian_Rejewski); what Alan Turing and Tommy Flowers did was automate the breaking, which was important because it had to be done again every day (due to the many combinations of configurations of the Enigma).
Tommy Flowers is known for Colossus which broke a different code, Lorenz.
https://en.wikipedia.org/wiki/Bombe cites Turing, Welchman and Rejewski.
Interesting how no other writers in the field seem to have adopted Knuths' strategy to get their books proofread to the point of being bullet proof.
No other writers have the stature of Knuth. The motivation to proof-read here is not the monetary reward after all.
Few other authors works have the legs to be reprinted sufficiently.
Bjarne Stroustrup did, at some point at least. I have a $32 real check from him for finding an error in "The C++ Programming Language (Special Edition)".
Sadly I think this is the end of an era. Someone should probably run an AI fact checker on this and send him the rest of any errors. Or he could change the nature or requirement of the reward, if somehow it can be proved the error could not have been found without a human's effort.
I'm not convinced you're right, but in the event, I wouldn't be sad about it, and I daresay Dr. Knuth would be delighted, rather than sad.
The Tex policy is that all bugs are to be fixed while Donald Knuth lives, after which the version becomes π and "all bugs are declared features".
Imagine if all the bugs just got fixed instead, and it was due to artificial intelligence! No, I don't think he'd mind at all. https://www-cs-faculty.stanford.edu/~knuth/papers/claude-cyc...
I know a guy (ricbit) who have 4 or more
I wonder if someone has used an LLM yet to analyze Knuth’s books and find errors to inundate him with? Please don’t do that (although I’m sure it’s possible).
people are up in arms about AI/LLMs now, but I'll bet 50 years ago Knuth would have been excited a about the prospect of algorithms being so capable.
Indeed he seems to be excited about it now, after Claude Opus 4.6 solved a problem he'd been working on: https://www-cs-faculty.stanford.edu/~knuth/papers/claude-cyc...
note "now" is April 2026
But what's the most Reward checks anyone has ever held?
Top entry:
https://www-cs-faculty.stanford.edu/~knuth/boss.html
thanks!
Although that omits the paper check era.
My guess for the top slot off the top of my head was actually #4.
Is that necessarily accurate?
> "These account balances reflect only the rewards for errors reported since the beginning of 2006. Many reward checks were issued during 1968--2005, too numerous to mention here."
There's 20 years on that chart vs 37 not on it.
Also that's "account balance" rather than "the most Reward checks" which I take to mean "the most [number of] reward checks" -- there's probably a correlation, yes, but [0] shows a variety of ways where check values are non-constant.
[0] https://en.wikipedia.org/wiki/Knuth_reward_check#Reward_amou...
There is only one person that can rule that out, but since this is their statement on the subject I would take it as authoritative unless there is a better source.
You probably have a substantial subset of the people on that list on HN, so it might be possible to recover a chunk of the 'paper era'.
I received two checks in the very early 2000s and my name isn’t on this list.
For the record I cashed both and have zero regrets. At the time it definitely felt like the right thing to do as I am not into collecting tokens.
Most rock and roll thing I heard today :)
> I would take it as authoritative unless there is a better source.
I'm not doubting the authority on the balances; it's the correlation to the number of checks I'm querying - high balance doesn't necessarily mean high number of checks, especially since the checks can have different values.
I doubt even Knuth has those records, so this is as good as it gets until someone sets off to compile a list of the 'paper past' that has enough proof to back the numbers.
> Is that necessarily accurate?
Udo's knowledge of TeX is absolutely stunning, so I would be very surprised if he weren't in first place. And DRF [0] [1] seemed to agree with the ranking in a sibling comment [2], which is also suggests that it's accurate.
> There's 20 years on that chart vs 37 not on it.
The reward values have increased exponentially over the years (I think?), so the older years should be relatively insignificant to the overall balances.
[0]: https://www.overleaf.com/blog/618-an-interview-with-david-fu...
[1]: https://tug.org/interviews/fuchs.html
[2]: https://news.ycombinator.com/item?id=50037551
Well, I'm #4, but it's all from TeX stuff (where I'm kind of a ringer), and not The Art Of Computer Programming. The beyond-amazing Udo Wermuth is also all TeX, I believe, and did it without having a home team advantage; everyone else high on the list looks to be strictly TAOCP.
curious, how do you pronounce the color fuchsia?
F-you-sh-uh
I like to use https://youglish.com/ when I have a question about English pronunciation.
Thank you, just a wonderful website for learning pronunciations!
Heh, and I thought I was being pedantic with my reward cheque. In my case I found inconsistent hyphenation in a technical term used in the book. I had wondered how to hyphenate it in my own writing so turned to Knuth to see what he did and was surprised to find it inconsistent even within a single volume of TAOCP! He wrote back with a funny message and a cheque for the back of San Serrif. It's on my wall now.
Just FYI for HN - if there is anyone looking to make big money in the coming years there are no fully signed TAOCP first editions anywhere. You would honestly print so much money if you could get all the first edition volumes signed.
He is incredibly generous with his signings --- even doing one on the spur of the moment in his home when one of the presenters mentioned that he'd been unable to source a copy of _Mathematical Fun and Games_ (I had a copy I'd planned on getting signed, but instead passed it to his wife and insisted that she get a photo of DEK signing it for her husband and that they keep it).
Interesting. I wonder if there is a way to get the completed volumes signed by him prior to shipping all the way to Australia. I was all over abesbooks looking for signed copies but couldn't find anything.
The thing is, the first editions were a _long_ while ago --- not sure how many are in good condition and for sale even unsigned.
Apparently some folks actually paid in advance for the full set leatherbound --- it'll be interesting to see the posts about Vol. 4 being delivered....
Images weren't loading for me, here's a Wayback Machine link https://web.archive.org/web/20260412143311/https://www.thoma...
Thank you for this! Images weren't loading for me, either.
The HN URL is missing the trailing slash; see https://news.ycombinator.com/item?id=50036221
We updated the URL to add the slash, thanks!
Can we adjust the URL to have a final trailing slash? The HN URL points to,
But this means the images, whose hrefs are like,
Don't load; that relative-ref results in a URL of
Which is a 404.
One can infer that the post's URI is like a "directory" of the subresources for the post, including those images; the URL of
(n.b. the trailing slash) adjusts the resolution of the image's relative-ref now to:
And the images load. Yes, trailing slashes in URLs are significant in the case of resolving a relative ref like that.
If the author is here, you might consider redirecting the non-slash to the slash.
> But why will you find me there with the entry “0x$1.20”, i.e. decimal $2.88?
I know Knuth has his own notation here, (it is clearly noted at the bottom of the BOSS page) but 0x1.20 should really be decimal 1.125.
Done, thanks!
i was expecting an article about farming these with claude.
thank god it wasn't that lol
True AGI will arrive when an LLM will be able to provide ALL remaining mistakes in Donald Knuth's books. And kill one more amazing thing in the process.