# ProofCouncil: An LLM Agent for Solving Open Mathematical Problems

arXiv: https://arxiv.org/abs/2607.09474 · HTML: https://mlsanity.com/paper/2607.09474/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Placed in Educational agents and math problem solving, one of 16 directions in LLM agents and tool use.
- Builds on 4 of its 15 references that are in the map.
- First posted on arXiv 10 Jul 2026.

## Placed in

- LLM agents and tool use / [Educational agents and math problem solving](https://mlsanity.com/agents/educational-agents-and-math-problem-solving/)

## Builds on (most cited first, 4 of 4)

- [First Proof](https://mlsanity.com/paper/2602.05192/) (2026)
- [Automated Conjecture Resolution with Formal Verification](https://mlsanity.com/paper/2604.03789/) (2026)
- [Project Aletheia: Verifier-Guided Distillation of Backtracking for Small Language Models](https://mlsanity.com/paper/2601.14290/) (2026)
- [RMA: an Agentic System for Research-Level Mathematical Problems](https://mlsanity.com/paper/2605.22875/) (2026)

## Built on by (most cited first, 7 of 7)

- [Albilich: Steerable Proof-State Orchestration for LLM-Based Mathematical Research with CAS Integration](https://mlsanity.com/paper/2607.27705/) (2026)
- [VALG: An Agentic System for ML Theory Research](https://mlsanity.com/paper/2608.13060/) (2026)
- [MECA: A Mechanism-Centered Agent for Constructing Well-Specified and Valuable Mathematical Conjectures](https://mlsanity.com/paper/2607.27709/) (2026)
- [Stellar Colosseum: A Many-Agent Harness for Long-Horizon Research in Mathematics and Theoretical Computer Science](https://mlsanity.com/paper/2609.15983/) (2026)
- [Andy: A Mathematical Agent for Rigorous Proof and Autonomous Research](https://mlsanity.com/paper/2608.15052/) (2026)
- [TCSAlgBench: Benchmarking Automated Proving for Research-Level Theoretical Computer Science](https://mlsanity.com/paper/2609.35606/) (2026)
- [Cogentic: Multi-Agent Orchestration for Automated Proof Discovery](https://mlsanity.com/paper/2609.40324/) (2026)

## Abstract (arXiv)

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.