Advancing Mathematics Research with AI-Driven Formal Proof Search

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 Ferraiuolo; Henryk Michalewski; Edward Lockhart; Codrut Grosu; Thomas Hubert; Matej Balog; Pushmeet Kohli; Swarat Chaudhuri

arXiv · 2605.22763

Advancing Mathematics Research with AI-Driven Formal Proof Search

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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 Erd\H{o}s 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 Erd\H{o}s 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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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 Ferraiuolo, Henryk Michalewski, Edward Lockhart, Codrut Grosu, Thomas Hubert, Matej Balog, Pushmeet Kohli, Swarat Chaudhuri. 2026-05-21. Advancing Mathematics Research with AI-Driven Formal Proof Search. https://arxiv.org/abs/2605.22763

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