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 designed to tackle open problems using an author-critic architecture.
ProofCouncil participated in 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 evaluated 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.
Blogger's Review: The success of ProofCouncil highlights the potential of LLMs in mathematics, particularly in addressing complex problems. The introduction of an agentic approach brings us closer to real mathematical research processes, offering new insights and tools for future mathematical automation.