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[Submitted on 17 Aug 2026]
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.
Submission history
From: Zeyu Zheng [view email]
[v1]
Mon, 17 Aug 2026 17:19:59 UTC (503 KB)
추출 본문 · 출처: arxiv.org · https://arxiv.org/abs/2608.16977