The Problem Is the Problem: Towards Scalable Mathematical Discovery

Details

AI-assisted mathematical discovery has typically relied on humans selecting specific problems upfront — a bottleneck as AI capabilities grow. This paper proposes a different model: supply a research direction rather than a specific problem, then let an automated cascade find, attempt, and recommend candidates for human attention. The Find-Attempt-Recommend (FAR) pipeline starts from a literature corpus, uses AI to recover candidate conjectures and open problems, filters for well-posed and still-open ones, and then applies reasoning and automated triage before surfacing a small subset for expert review. In a combinatorics pilot, 5,245 papers yielded 6,453 candidate conjectures, filtered to 4,717 apparently open ones, with 598 potential resolutions and 77 items for author-team review. Among the reviewed items, the team reports real discoveries, including results on conjectures from Davies-Jenssen-Perkins-Roberts, Erdős-Straus, Ikenmeyer-Pak-Panova, and Lund-Saraf-Wolf. Code is publicly available. The key contribution is architectural: allocating scarce human expert time and frontier-model compute to filtering and triage rather than exhaustive review. This points toward AI-in-the-loop research workflows where the bottleneck shifts from finding interesting problems to reviewing strong candidate proofs.