ProofCouncil: An LLM Agent for Solving Open Mathematical Problems
2026-07-10 • Artificial Intelligence
Artificial Intelligence
AI summaryⓘ
The authors created ProofCouncil, a computer program designed to solve tough math problems by working like a team of authors and critics. They tested it on a contest with 10 real math problems, and it solved 6 of them very well, better than other teams. They also tried it on 30 other open math problems, where it fully solved 5, showed promise in 2, and made useful progress on 8. The authors explain how they built ProofCouncil and shared the code for others to use.
large language modelsmathematical agentauthor-critic architectureopen mathematical problemsautonomous problem solvingmathematical proofsagentic workflowsFirstProof challengehuman feedbackopen source
Authors
Johannes Schmitt, Tim Gehrunger, Jasper Dekoninck, Gergely Bérczi, Uri Kreitner, Liam Price, David Holmes
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.