[2607.09474] ProofCouncil: An LLM Agent for Solving Open Mathematical Problems

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arXiv:2607.09474 (cs)

[Submitted on 10 Jul 2026]

Title:ProofCouncil: An LLM Agent for Solving Open Mathematical Problems

Authors:Johannes Schmitt, Tim Gehrunger, Jasper Dekoninck, Gergely Bérczi, Uri Kreitner, Liam Price, David Holmes<br>View a PDF of the paper titled ProofCouncil: An LLM Agent for Solving Open Mathematical Problems, by Johannes Schmitt and 6 other authors

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Abstract:Large language models (LLMs) have shown increasing promise in solving open problems in mathematics. However, their performance can be further improved through agentic workflows tailored to real-world mathematical practice. To this end, we introduce ProofCouncil, a mathematical agent that is designed to tackle open problems using an author-critic architecture. ProofCouncil served as a submission to the second batch of FirstProof, a challenge consisting of 10 real-world mathematical problems that agents must solve autonomously. Its submissions for 6 of the 10 problems were judged by the referees to be correct up to at most minor revisions, showing the best performance among participating teams. We also evaluate ProofCouncil on 30 open problems collected from mathematical researchers. Among the 21 solutions that received human feedback, 5 were judged completely correct, 2 more were judged promising pending final verification, and a further 8 contained useful partial progress. In this short paper, we describe the development of ProofCouncil and the agent-building library used to create it, which we release as open source to the community.

Comments:<br>25 pages, 7 figures. ProofCouncil appears as System A (IMProofBench ProofCouncil) in the official FirstProof second-batch report (arXiv:2606.18119). Code and agent-building library: this https URL

Subjects:

Artificial Intelligence (cs.AI)

Cite as:<br>arXiv:2607.09474 [cs.AI]

(or<br>arXiv:2607.09474v1 [cs.AI] for this version)

https://doi.org/10.48550/arXiv.2607.09474

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arXiv-issued DOI via DataCite

Submission history<br>From: Johannes Schmitt [view email]<br>[v1]<br>Fri, 10 Jul 2026 14:46:01 UTC (1,070 KB)

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