Google’s artificial intelligence systems AlphaProof and AlphaGeometry 2 have achieved breakthrough achievements, successfully solving four of six problems in the 2024 International Mathematical Olympics (IMO) and scoring a silver medal equivalent. This is the first time that an artificial intelligence system has achieved such a high level of performance in this prestigious competition.
AlphaProof is a reinforcement learning system that solves two algebraic problems and one number theory problem, including the most challenging topics in this competition. AlphaGeometry 2 is an improved version of its predecessor that solves geometry problems. These artificial intelligence systems scored a total of 28 points, with full marks for each problem solved.
Since 1959, the annual IMO is an important event for young mathematicians. This year, 58 of a total of 609 contestants won the gold medal with scores of 29 points or higher.
AlphaProof is a formal mathematical reasoning system based on reinforcement learning that can prove the correctness of mathematical statements. It combines a pre-trained language model with the AlphaZero reinforcement learning algorithm, using the formal language Lean for training and reasoning.
AlphaGeometry 2 is an improved version of the geometry problem solving system that uses a neural symbol mixing method and is trained on a large amount of synthetic data. The system solves geometric problems faster and more efficiently.
Introduction to the International Mathematical Olympics: IMO is the oldest, largest and most prestigious youth mathematics competition, attracting the world’s top pre-scientists to participate every year.
Model performance: In this year’s IMO, AlphaProof and AlphaGeometry 2 solved a total of four problems and scored 28 points, which is comparable to the results of the silver medalist.
How AlphaProof works: By training millions of mathematical problems, AlphaProof generates and validates solutions that strengthen the reasoning capabilities of its language models.
Improvements to AlphaGeometry 2: With a faster symbol engine and knowledge-sharing mechanism, AlphaGeometry 2 solves more complex geometry problems in less time.
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Original text:https://deepmind.google/discover/blog/ai-solves-imo-problems-at-silver-medal-level/
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