The Problem Is the Problem: Towards Scalable Mathematical Discovery

• URL: http://arxiv.org/abs/2608.16977v1
• Date: Mon, 17 Aug 2026 17:19:59 GMT
• Title: The Problem Is the Problem: Towards Scalable Mathematical Discovery
• Abstract summary: We build a literature-to-review cascade that automates the search for suitable problems and focuses human attention on artifacts that have passed several stages of filtering.<n>We identify many interesting discoveries, including results on conjectures and questions of Davies--Jenssen-Perkins--Roberts, Erds--Straus, Ikenmeyer--Pak--Panova, and Lund-Saraf--Wolf.
• Score: 27.74875048771945
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: AI systems are increasingly capable of contributing to mathematical research. In research practice, frontier-model reasoning is a limited resource, and expert mathematical review is even more sharply constrained. Allocating these scarce resources well is therefore central to making AI-assisted mathematical discovery efficient. In most current AI-for-math workflows, human effort is concentrated at the beginning and end, in selecting suitable research problems and later reviewing the resulting artifacts. These two stages are becoming bottlenecks for research-level mathematics. We address them by proposing a new human-AI discovery paradigm. The human input is no longer a single problem selected in advance, but a research direction in which the experts have interest and expertise. The system then searches a broad literature corpus for candidate problems in that direction. Inspired by search and recommender systems, we build Find, Attempt, and Recommend (FAR), a literature-to-review cascade that automates the search for suitable problems and focuses human attention on artifacts that have passed several stages of filtering. In a combinatorics pilot, the pipeline starts from 5,245 combinatorics papers, recovers 6,453 candidate conjectures or open problems, and filters them to 4,717 apparently well-posed and still-open conjectures. Subsequent reasoning and automated triage stages surface 598 potential resolutions and select 77 items for author-team review. Among them, we identify many interesting discoveries, including results on conjectures and questions of Davies--Jenssen--Perkins--Roberts, Erdős--Straus, Ikenmeyer--Pak--Panova, and Lund--Saraf--Wolf. These results demonstrate the effectiveness of this new mode of human-AI collaboration for mathematical discovery.

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