An AI system matched gold-medal-level performance on 2025 math olympiad problems

The system combined informal problem-solving with formally checked proofs in the Lean proof assistant.

Editorial illustration — not from the study.

The researchers introduced Aristotle, a system designed to solve advanced mathematical problems and produce formal proofs. It combines a Lean proof-search system with an informal reasoning system that generates and formalizes lemmas, as well as a dedicated geometry solver.

According to the abstract, Aristotle reached gold-medal-equivalent performance on the 2025 International Mathematical Olympiad problems. The researchers also report state-of-the-art performance in automated theorem proving and favorable scaling properties, though the abstract does not define those measures in detail.

How Aristotle performed

Aristotle achieved gold-medal-equivalent performance on the 2025 International Mathematical Olympiad problems. Its approach combined three components: a Lean proof-search system, an informal reasoning system that generates and formalizes lemmas, and a dedicated geometry solver. The system used formal verification alongside informal reasoning, so its mathematical solutions could be checked in a formal proof system.

Why formal proofs matter

The result suggests that automated theorem-proving systems can combine the flexible idea generation used in informal mathematics with the strict checking of formal proofs. That combination is relevant to efforts to make computer-generated mathematical reasoning both capable on difficult problems and independently verifiable.

Evidence and caveats

This is a research article reporting the performance of an AI system on International Mathematical Olympiad problems and in automated theorem proving. The abstract does not give the evaluation procedure, individual problem results, comparison details, or a precise definition of the claimed scaling properties. It also does not establish how well Aristotle would perform on mathematical problems outside the tested tasks.

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