ProofCouncil: An LLM Agent for Solving Open Mathematical Problems
Quick Answer
ProofCouncil is an advanced LLM agent that effectively addresses open mathematical problems using an author-critic architecture, achieving correct solutions for 6 out of 10 challenges in the FirstProof competition.
Quick Take
ProofCouncil is an advanced LLM agent that effectively addresses open mathematical problems using an author-critic architecture, achieving correct solutions for 6 out of 10 challenges in the FirstProof competition. It also demonstrated strong performance on 30 additional open problems, with 5 solutions deemed completely correct. The agent-building library is released as open source.
Key Points
- ProofCouncil achieved the best performance in the FirstProof competition among participating teams.
- It solved 6 out of 10 real-world mathematical problems with minor revisions.
- Out of 30 evaluated open problems, 5 solutions were completely correct.
- The agent-building library for ProofCouncil is available as open source.
- ProofCouncil employs an author-critic architecture for enhanced problem-solving.
Paper Resources
📖 Reader Mode
~2 min readAbstract: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: | 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: | arXiv:2607.09474 [cs.AI] |
| (or arXiv:2607.09474v1 [cs.AI] for this version) | |
| https://doi.org/10.48550/arXiv.2607.09474 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Johannes Schmitt [view email]
[v1]
Fri, 10 Jul 2026 14:46:01 UTC (1,070 KB)
— Originally published at arxiv.org
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