{"slug": "advancing-mathematics-research-with-ai-driven-formal-proof-search", "title": "Advancing mathematics research with AI-driven formal proof search", "summary": "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.", "body_md": "# Computer Science > Artificial Intelligence\n\n[Submitted on 21 May 2026]\n\n# Title:Advancing Mathematics Research with AI-Driven Formal Proof Search\n\n[View PDF](/pdf/2605.22763)\n\n[HTML (experimental)](https://arxiv.org/html/2605.22763v1)\n\nAbstract: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.\n\n## Submission history\n\nFrom: Swarat Chaudhuri [[view email](/show-email/0bf3cfd0/2605.22763)]\n\n**[v1]** Thu, 21 May 2026 17:24:57 UTC (1,291 KB)\n\n### References & Citations\n\nLoading...\n\n# Bibliographic and Citation Tools\n\nBibliographic Explorer\n\n*(*[What is the Explorer?](https://info.arxiv.org/labs/showcase.html#arxiv-bibliographic-explorer))\nConnected Papers\n\n*(*[What is Connected Papers?](https://www.connectedpapers.com/about))\nLitmaps\n\n*(*[What is Litmaps?](https://www.litmaps.co/))\nscite Smart Citations\n\n*(*[What are Smart Citations?](https://www.scite.ai/))# Code, Data and Media Associated with this Article\n\nalphaXiv\n\n*(*[What is alphaXiv?](https://alphaxiv.org/))\nCatalyzeX Code Finder for Papers\n\n*(*[What is CatalyzeX?](https://www.catalyzex.com))\nDagsHub\n\n*(*[What is DagsHub?](https://dagshub.com/))\nGotit.pub\n\n*(*[What is GotitPub?](http://gotit.pub/faq))\nHugging Face\n\n*(*[What is Huggingface?](https://huggingface.co/huggingface))\nScienceCast\n\n*(*[What is ScienceCast?](https://sciencecast.org/welcome))# Demos\n\n# Recommenders and Search Tools\n\nInfluence Flower\n\n*(*[What are Influence Flowers?](https://influencemap.cmlab.dev/))\nCORE Recommender\n\n*(*[What is CORE?](https://core.ac.uk/services/recommender))# arXivLabs: experimental projects with community collaborators\n\narXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.\n\nBoth 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.\n\nHave an idea for a project that will add value for arXiv's community? [ Learn more about arXivLabs](https://info.arxiv.org/labs/index.html).", "url": "https://wpnews.pro/news/advancing-mathematics-research-with-ai-driven-formal-proof-search", "canonical_source": "https://arxiv.org/abs/2605.22763", "published_at": "2026-05-25 18:44:45+00:00", "updated_at": "2026-05-25 19:08:15.828580+00:00", "lang": "en", "topics": ["artificial-intelligence", "large-language-models", "ai-agents"], "entities": ["Swarat Chaudhuri", "Lean", "Erdős", "OEIS"], "alternates": {"html": "https://wpnews.pro/news/advancing-mathematics-research-with-ai-driven-formal-proof-search", "markdown": "https://wpnews.pro/news/advancing-mathematics-research-with-ai-driven-formal-proof-search.md", "text": "https://wpnews.pro/news/advancing-mathematics-research-with-ai-driven-formal-proof-search.txt", "jsonld": "https://wpnews.pro/news/advancing-mathematics-research-with-ai-driven-formal-proof-search.jsonld"}}