Fig. 2: AlphaGeometry advances the current state of geometry theorem prover from below human level to near gold-medallist level.
From: Solving olympiad geometry without human demonstrations
The test benchmark includes official IMO problems from 2000 to the present that can be represented in the geometry environment used in our work. Human performance is estimated by rescaling their IMO contest scores between 0 and 7 to between 0 and 1, to match the binary outcome of failure/success of the machines. For example, a contestant’s score of 4 out of 7 will be scaled to 0.57 problems in this comparison. On the other hand, the score for AlphaGeometry and other machine solvers on any problem is either 0 (not solved) or 1 (solved). Note that this is only an approximate comparison with humans on classical geometry, who operate on natural-language statements rather than narrow, domain-specific translations. Further, the general IMO contest also includes other types of problem, such as geometric inequality or combinatorial geometry, and other domains of mathematics, such as algebra, number theory and combinatorics.
