Advancing Mathematics Research with AI-Driven Formal Proof Search
A new paper presents the first large-scale evaluation of using large language models to generate formal proofs for solving open mathematical problems. The most capable agent autonomously resolved 9 of 353 open Erdős problems at a cost of a few hundred dollars per problem, proved 44 out of 492 OEIS conjectures, and is being deployed in combinatorics, optimization, graph theory, algebraic geometry, and quantum optics. The findings demonstrate the power of AI-aided formal proof search.
Article intelligence
Key points
- First large-scale evaluation of LLM-generated formal proofs for open problems
- Most capable agent solved 9 Erdős problems at ~$100/problem
- Agent proved 44 OEIS conjectures and deployed in multiple fields
- AI-aided formal proof search shows promise for mathematics research
Why it matters
This matters because first large-scale evaluation of LLM-generated formal proofs for open problems.
Technical impact
May affect model selection, inference cost, product capability, and evaluation benchmarks.
[2605.22763] Advancing Mathematics Research with AI-Driven Formal Proof Search
[Submitted on 21 May 2026]
Title:Advancing Mathematics Research with AI-Driven Formal Proof Search
View a PDF of the paper titled Advancing Mathematics Research with AI-Driven Formal Proof Search, by George Tsoukalas and 19 other authors
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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.
Comments: The first three authors and the last author have equal contributions. The first three authors are in random order
Subjects:
Artificial Intelligence (cs.AI)
Cite as: arXiv:2605.22763 [cs.AI]
(or arXiv:2605.22763v1 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2605.22763
arXiv-issued DOI via DataCite (pending registration)
Submission history
From: Swarat Chaudhuri [view email] [v1] Thu, 21 May 2026 17:24:57 UTC (1,291 KB)
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