AI Mathematician: Towards Fully Automated Frontier Mathematical Research

TL;DR

This paper introduces the AI Mathematician framework that leverages large reasoning models to support and automate frontier mathematical research, addressing complexity and procedural rigor challenges.

Contribution

The paper presents a novel AI framework that enhances LRM capabilities for research-level mathematics through exploration and verification strategies.

Findings

AIM can autonomously construct substantial proofs.

AIM uncovers non-trivial insights in mathematical research areas.

Experimental results show promising potential for AI in mathematical discovery.

Abstract

Large Reasoning Models (LRMs) have made significant progress in mathematical capabilities in recent times. However, these successes have been primarily confined to competition-level problems. In this work, we propose AI Mathematician (AIM) framework, which harnesses the reasoning strength of LRMs to support frontier mathematical research. We have identified two critical challenges of mathematical research compared to competition, {\it the intrinsic complexity of research problems} and {\it the requirement of procedural rigor}. To address these challenges, AIM incorporates two core strategies: an exploration mechanism to foster longer solution paths, and the pessimistic reasonable verification method to ensure reliability. This early version of AIM already exhibits strong capability in tackling research-level tasks. We conducted extensive experiments across several real-world mathematical topics and obtained promising results. AIM is able to autonomously construct substantial portions of proofs and uncover non-trivial insights within each research area. These findings highlight the potential of LRMs in mathematical discovery and suggest that LRM-based agent systems could significantly accelerate mathematical research in the future.