用文献搜索自动找数学难题,让人类专注高价值发现。
The Problem Is the Problem: Towards Scalable Mathematical Discovery

- 人类提供研究方向,系统从5245篇论文中挖掘候选问题
- 经多轮筛选后产出77个待审成果,其中含多个重要发现
- 适合想高效探索新数学领域的研究者使用
AI在数学研究中的作用日益增强。前沿模型推理和专家评审均属稀缺资源,如何高效分配至关重要。当前AI数学工作流中,人类精力集中在问题选取和结果审查,已成为瓶颈。为此提出新型人机协作范式:人类不再预设具体问题,而是提供感兴趣的研究方向。系统基于文献库自动搜寻相关候选问题。受搜索与推荐系统启发,构建了文献到评审的级联流程FAR,实现问题搜索自动化,并将人力聚焦于已通过多阶段过滤的成果。在组合数学试点中,从5,245篇论文出发,提取6,453个候选猜想或开放问题,筛选出4,717个看似合理且未解的问题;后续推理与自动甄别阶段发现598个潜在解法,最终选定77项供作者团队评审。其中包含对Davies--Jenssen--Perkins--Roberts、Erdős--Straus、Ikenmeyer--Pak--Panova及Lund--Saraf--Wolf等猜想的重要进展,验证了该协作模式的有效性。
原文摘要 · Abstract (English)
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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