ProofCouncil: An LLM Agent for Solving Open Mathematical Problems

Researchers introduced ProofCouncil, an LLM-based agent using an author-critic architecture to solve open mathematical problems. In the FirstProof challenge, it correctly solved 6 of 10 problems, outperforming other teams, and on 30 open problems, 5 solutions were judged completely correct. The agent and its open-source library aim to advance AI-assisted mathematical research.

arXiv:2607.09474v1 Announce Type: new 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.