points by fovc 2 years ago

As a consumer of those problems, first of all, thank you! Even decades on from high school I occasionally enjoy working on them.

But agree that geometry was obviously going to be first. From what I’ve gathered here, it’s not “brute forcing” in terms of relying on algebraic geometry, vectors, or complex number solutions, but it is brute force in that it’s exhaustively looking for “interesting” constructions.

Geometry was always my worst subject, but even so I felt like if given the right construction the problem was much easier. Unfortunately I never developed the intuition to hit on those constructions quickly. It seems this AI doesn’t either, but it can churn through them much faster — There are only so many perpendiculars and parallels and bisectors you can construct which you can more or less mechanically evaluate (map out all angles and ratios, try power of a point, etc.)

While this is incredibly impressive, it seems like Deep Mind:Kasparov::AlphaGeo:Terry Tao in the “engine vs AI” sense.

I agree Algebra is likely next. Like geometry, more often than not you “just” need a clever substitution or 3, of which there are only so many options to choose from.

Some combinatorics problems I think would also be amenable to this search strategy (e.g., finding things to count 2 ways), but that seems like a bridge further away, and only gets you a subset of problems.

Number theory would be my guess for the final frontier before a perfect 42.