The Problem Is the Problem: Towards Scalable Mathematical Discovery

问题即问题：迈向可扩展的数学发现

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.

摘要： 人工智能系统在数学研究中的贡献能力日益增强。在研究实践中，前沿模型的推理能力是一种有限资源，而专家级的数学评审则受到更严格的限制。因此，如何合理分配这些稀缺资源，对于提高人工智能辅助数学发现的效率至关重要。

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.

在当前大多数“人工智能辅助数学”的工作流程中，人类的精力主要集中在流程的起点和终点，即选择合适的研究问题以及后续对研究成果进行评审。这两个阶段正逐渐成为研究级数学发展的瓶颈。我们通过提出一种新的人机协作发现范式来解决这些问题。

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.

人类的输入不再是预先选定的单一问题，而是专家感兴趣且具备专业知识的研究方向。随后，系统会在广泛的文献库中搜索该方向的候选问题。受搜索和推荐系统的启发，我们构建了“查找、尝试与推荐”（Find, Attempt, and Recommend, FAR）系统。这是一个从文献到评审的级联流程，能够自动搜索合适的问题，并将人类的注意力集中在经过多轮筛选的成果上。

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.

在一项组合数学的试点研究中，该流程从 5,245 篇组合数学论文出发，提取出 6,453 个候选猜想或开放性问题，并将其筛选为 4,717 个表述清晰且尚未解决的猜想。随后的推理和自动分类阶段筛选出了 598 个潜在的解决方案，并最终选出 77 个项目供研究团队评审。

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.

在这些项目中，我们发现了许多有趣的成果，包括针对 Davies—Jenssen—Perkins—Roberts、Erdős—Straus、Ikenmeyer—Pak—Panova 以及 Lund—Saraf—Wolf 等人的猜想和问题的研究结果。这些成果证明了这种新的人机协作模式在数学发现中的有效性。