RMA: an Agentic System for Research-Level Mathematical Problems

2026-05-20

AI Summary

This work addresses the challenges of long-horizon reasoning, reliance on mathematical literature, and iterative proof refinement inherent in research-level theorem proving by introducing the first multi-agent collaborative framework tailored for this domain. The proposed system orchestrates multiple rounds of interaction among initializer, proposer, and verifier agents, integrating structured memory, literature comprehension, and dynamic knowledge base construction. Evaluated on the First Proof benchmark, it successfully solves 8 out of 10 expert-level problems, substantially outperforming strong baselines such as GPT-5.2R and Aletheia. While preserving logical rigor, the method enhances proof readability and overall quality, thereby transcending the limitations of traditional competition mathematics and formalized proof systems.

Abstract

We present $\textbf{Research Math Agents (RMA)}$, an agentic framework for automated reasoning on research-level mathematical problems. Unlike prior studies centered on competition mathematics or formal theorem proving, RMA targets research-level mathematical problems that require long-horizon reasoning, literature grounding, and iterative proof refinement. RMA decomposes research-level proof solving into specialized modules for problem analysis, literature search and understanding, fair comparison, knowledge-bank construction, and proof verification, all coordinated by initializer, proposer, and verifier agents through a shared structured memory. Within this unified framework, these agents operate in a multi-role, multi-round workflow, collaboratively generating, refining, and verifying candidate proofs through iterative feedback. We evaluate RMA on the First Proof benchmark, which consists of ten research-level problems contributed by expert mathematicians across diverse domains. Through comprehensive expert evaluation, RMA outperforms strong baselines on the First Proof benchmark, including GPT-5.2R and Aletheia, solving eight out of ten research problems and producing more logically sound and readable proofs. Our comprehensive ablation studies further show that performance gains arise from the interaction of structured reasoning modules, iterative refinement, and verifier-based feedback, rather than any single component. Our solutions and implementations will be made publicly available upon acceptance.

Problem

• research-level mathematical problems
• long-horizon reasoning
• literature grounding
• iterative proof refinement
• automated reasoning

Innovation

• agentic system
• research-level mathematics
• iterative proof refinement
• structured memory
• multi-agent collaboration