Advancing Mathematics Research with AI-Driven Formal Proof Search

• URL: http://arxiv.org/abs/2605.22763v1
• Date: Thu, 21 May 2026 17:24:57 GMT
• Title: Advancing Mathematics Research with AI-Driven Formal Proof Search
• Abstract summary: Large language models (LLMs) increasingly excel at mathematical reasoning, but their unreliability limits their utility in mathematics research.<n>A mitigation is using LLMs to generate formal proofs in languages like Lean.<n>We perform the first large-scale evaluation of this method's ability to solve open problems.
• Score: 20.297700405590156
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Large language models (LLMs) increasingly excel at mathematical reasoning, but their unreliability limits their utility in mathematics research. A mitigation is using LLMs to generate formal proofs in languages like Lean. We perform the first large-scale evaluation of this method's ability to solve open problems. Our most capable agent autonomously resolved 9 of 353 open Erdős problems at the per-problem cost of a few hundred dollars, proved 44/492 OEIS conjectures, and is being deployed in combinatorics, optimization, graph theory, algebraic geometry, and quantum optics research. A basic agent alternating LLM-based generation with Lean-based verification replicated the Erdős successes but proved costlier on the hardest problems. These findings demonstrate the power of AI-aided formal proof search and shed light on the agent designs that enable it.

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