The Problem Is the Problem: Towards Scalable Mathematical Discovery

Summary

AI systems are increasingly contributing to mathematical research, but frontier-model reasoning and expert review are scarce resources that must be allocated efficiently. Current AI-for-math workflows concentrate human effort on problem selection and artifact review, which are becoming bottlenecks. To address this, the authors propose a new human-AI discovery paradigm in which humans specify a research direction, and the system searches a large literature corpus for candidate problems. They build Find, Attempt, and Recommend (FAR), a literature-to-review cascade. In a combinatorics pilot, the pipeline starts from 5,245 papers, recovers 6,453 candidate conjectures or open problems, filters to 4,717 apparently well-posed and still-open conjectures, surfaces 598 potential resolutions, and selects 77 for author-team review. Among these, they identify discoveries related to conjectures by Davies–Jenssen–Perkins–Roberts, Erdős–Straus, Ikenmeyer–Pak–Panova, and Lund–Saraf–Wolf, demonstrating the effectiveness of this new mode of human-AI collaboration.