| title | The Problem Is the Problem: Towards Scalable Mathematical Discovery |
|---|---|
| authors | Zeyu Zheng, Shengtong Zhang, Jeremy Avigad, Prasad Tetali, Sean Welleck |
| date | 2026-08-17 |
| venue | arXiv (preprint, not peer reviewed) |
| id | arXiv:2608.16977 |
| affiliation | Carnegie Mellon University |
| upvotes | 7 (Hugging Face Daily Papers, 2026-11-01) |
| links | abs pdf hf code |
| 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. |
cite
@misc{zheng2026problem,
title={The Problem Is the Problem: Towards Scalable Mathematical Discovery},
author={Zeyu Zheng and Shengtong Zhang and Jeremy Avigad and Prasad Tetali and Sean Welleck},
year={2026},
eprint={2608.16977},
archivePrefix={arXiv},
url={https://arxiv.org/abs/2608.16977}
}