Re:AI solves IMO problems at silver medal level
by visarga on Thursday July 25, 2024 @01:10PM
(#41070984)
Euclidian Geometry still requires constructions to solve, and those are based in intuition.
Re:AI solves IMO problems at silver medal level
by gjm11 on Thursday July 25, 2024 @05:03PM
(#41073355)
There are known algorithms that can solve _all_ problems in euclidean (ruler-and-compasses) geometry, no intuition required. The most effective algorithms of this type are quite inefficient, though, and (at least according to DeepMind) don't do as well as AlphaGeometry does at e.g. IMO geometry problems.
So either (1) "within minutes" was underselling the abilities of the system, or (2) what they actually meant was that the geometry problem was solved in 19 seconds, one of the others "within minutes" (I'd guess #1 which is definitely easier than the other two they solved), and the others in unspecified times of which the longer was ~3 days.
I'd guess it's the first of those.
(Euclidean geometry has been a kinda-solved domain for some time; it's not super-surprising that they were able to solve that problem quickly.)
As for the long solve times, I would guess they're related to this fascinating remark:
> The training loop was also applied during the contest, reinforcing proofs of self-generated variations of the contest problems until a full solution could be found.