AlphaGeometry (neural network)

2024: Runner-up at the Mathematics Olympiad

On July 25, 2024, Google DeepMind, a company specializing in artificial intelligence research, unveiled AlphaProof and AlphaGeometry 2 AI models capable of handling complex math tasks. Together they were able to solve four of the six problems of the International Mathematical Olympiad (IMO), which corresponds to the second place - a silver medal.

AlphaProof is a system that is trained to prove mathematical statements in the formal Lean language. It combines a pre-trained language model with the AlphaZero reinforcement learning algorithm, which previously taught itself to play chess, segi and go. In turn, AlphaGeometry 2 is an advanced version of the AlphaGeometry AI system, which is designed to solve geometry problems. It is a neurosymbol hybrid system in which the language model is based on Gemini and trained on a large amount of synthetic data.

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Each of the six IMO tasks can earn seven points, and the overall maximum is 42 points. The combination of AlphaProof and AlphaGeometry 2 models showed a result of 28 points, receiving the maximum score for each of the four solved problems. In particular, AlphaProof coped with two algebraic tasks and one task in number theory, issuing an answer and proving it correct. AlphaGeometry 2 solved one geometry problem. At the same time, two tasks in combinatorics remained unresolved.

It is emphasized that AlphaProof coped with one of the most difficult tasks at the Olympics, which only five IMO participants were able to master. New AI models lacked just one point to reach the gold medal threshold. At the official competition, 58 out of 609 participants were able to overcome the bar of 29 points. Thus, for the first time, AI in solving mathematical problems, IMO was able to show results at the level of medalists.^[1]

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