ProofCouncil is an LLM-based mathematical research agent that combines proof authorship and criticism to address open problems. Its workflow is designed around mathematical research practice. In the second batch of the FirstProof challenge, referees assessed its solutions to six of ten problems as correct or requiring only minor revisions, the strongest result among participating teams. The paper also reports experiments on 30 open problems supplied by researchers. Human feedback was available for 21 solutions: five were considered fully correct, two showed promise but awaited final verification, and eight made useful partial progress. The authors describe the agent’s development and release both ProofCouncil and its underlying agent-building library as open source.
@misc{schmitt2026proofcouncilllmagentsolving, title={ProofCouncil: An LLM Agent for Solving Open Mathematical Problems}, author={Johannes Schmitt and Tim Gehrunger and Jasper Dekoninck and Gergely Bérczi and Uri Kreitner and Liam Price and David Holmes}, year={2026}, eprint={2607.09474}, archivePrefix={arXiv}, primaryClass={cs.AI}, url={https://arxiv.org/abs/2607.09474} }