Advancing mathematics research with AI-driven formal proof search

Researchers have demonstrated that AI agents using large language models to generate formal proofs in Lean can autonomously solve open mathematics problems, resolving 9 of 353 unsolved Erdős problems at a cost of a few hundred dollars per problem and proving 44 of 492 OEIS conjectures. The approach, which alternates LLM-based proof generation with verification in the Lean formal proof language, is now being deployed across combinatorics, optimization, graph theory, algebraic geometry, and quantum optics research. The findings establish AI-aided formal proof search as a viable tool for advancing mathematics research by overcoming the unreliability of LLMs in mathematical reasoning.

Computer Science Artificial Intelligence Submitted on 21 May 2026 Title:Advancing Mathematics Research with AI-Driven Formal Proof Search View PDF /pdf/2605.22763 HTML experimental https://arxiv.org/html/2605.22763v1 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. Submission history From: Swarat Chaudhuri view email /show-email/0bf3cfd0/2605.22763 v1 Thu, 21 May 2026 17:24:57 UTC 1,291 KB References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer What is the Explorer? https://info.arxiv.org/labs/showcase.html arxiv-bibliographic-explorer Connected Papers What is Connected Papers? https://www.connectedpapers.com/about Litmaps What is Litmaps? https://www.litmaps.co/ scite Smart Citations What are Smart Citations? https://www.scite.ai/ Code, Data and Media Associated with this Article alphaXiv What is alphaXiv? https://alphaxiv.org/ CatalyzeX Code Finder for Papers What is CatalyzeX? https://www.catalyzex.com DagsHub What is DagsHub? https://dagshub.com/ Gotit.pub What is GotitPub? http://gotit.pub/faq Hugging Face What is Huggingface? https://huggingface.co/huggingface ScienceCast What is ScienceCast? https://sciencecast.org/welcome Demos Recommenders and Search Tools Influence Flower What are Influence Flowers? https://influencemap.cmlab.dev/ CORE Recommender What is CORE? https://core.ac.uk/services/recommender arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs https://info.arxiv.org/labs/index.html .