[Research Press Release] Artificial intelligence: A mathematics medal-worthy AI system (Nature)

An AI system that can prove complex mathematical theories is described in Nature this week. The system, Google DeepMind’s AlphaProof, has achieved a silver medal-worthy performance at the 2024 International Mathematics Olympiad (IMO).

Mathematicians use computational tools to solve complex problems and prove theories. AI systems could possibly speed up this process. While some large language models have shown promising capabilities, it has been difficult to verify the correctness of their reasoning as they are trained and operate on informal, natural-language text. Researchers at Google DeepMind show how reinforcement learning can be made to work within a formal mathematics software environment (known as Lean) to generate proofs whose reasoning can be automatically verified, potentially overcoming this challenge.

AlphaProof is designed to prove mathematical statements. It learns to find these proofs through reinforcement learning, after auto-formalizing 80 million statements to use for training. The system is shown to improve on results from previous state-of-the-art AI systems for historical mathematics competition problems. In 2024, AlphaProof tackled complex problems from the IMO, a prestigious high-school-level mathematics competition. AlphaProof, combined with a geometry-solving system called AlphaGeometry, solved four out of six problems from the competition, achieving a score equivalent to that of a silver medallist.

While AlphaProof has demonstrated impressive performance in the domain of competition-level mathematical reasoning, the authors note some limitations in solving other forms of difficult problems, which they suggest as avenues for future research. They conclude that addressing these limitations will pave the way for AlphaProof to become a valuable tool in complex mathematical problem solving. 

• Article
• Published: 12 November 2025

Hubert, T., Mehta, R., Sartran, L. et al. Olympiad-level formal mathematical reasoning with reinforcement learning. Nature (2025). https://doi.org/10.1038/s41586-025-09833-y

News & Views: Mathematicians put AI model AlphaProof to the test
https://www.nature.com/articles/d41586-025-03585-5

© 2025 Springer Nature Limited. All Rights Reserved.  

More Press Releases