[2605.22763] Advancing Mathematics Research with AI-Driven Formal Proof Search

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Computer Science > Artificial Intelligence

arXiv:2605.22763 (cs)

[Submitted on 21 May 2026]

Title:Advancing Mathematics Research with AI-Driven Formal Proof Search

Authors:George Tsoukalas, Anton Kovsharov, Sergey Shirobokov, Anja Surina, Moritz Firsching, Gergely Bérczi, Francisco J. R. Ruiz, Arun Suggala, Adam Zsolt Wagner, Eric Wieser, Lei Yu, Aja Huang, Miklós Z. Horváth, Andrew Ferrauiolo, Henryk Michalewski, Codrut Grosu, Thomas Hubert, Matej Balog, Pushmeet Kohli, Swarat Chaudhuri<br>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:<br>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:<br>arXiv:2605.22763 [cs.AI]

(or<br>arXiv:2605.22763v1 [cs.AI] for this version)

https://doi.org/10.48550/arXiv.2605.22763

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arXiv-issued DOI via DataCite (pending registration)

Submission history<br>From: Swarat Chaudhuri [view email]<br>[v1]<br>Thu, 21 May 2026 17:24:57 UTC (1,291 KB)

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