问题本身才是问题：迈向可扩展的数学发现
The Problem Is the Problem: Towards Scalable Mathematical Discovery
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中文总结 AI 辅助
该研究提出人机协作的FAR流程，从文献中筛选数学问题并聚焦成果，在组合数学试点中筛选出77个待评审成果，验证了其数学发现的有效性。
中文摘要 AI 辅助
AI系统越来越有能力为数学研究做出贡献。在研究实践中，前沿模型推理是有限的资源，而专家数学评审的约束则更为严格。因此，合理分配这些稀缺资源对于提高AI辅助数学发现的效率至关重要。在当前大多数面向数学的AI工作流程中，人力集中在流程的开始和结束阶段，即选择合适的研究问题以及后续对成果进行评审。这两个阶段正成为研究级数学的瓶颈。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。人类的输入不再是预先选定的单个问题，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语料库中搜索该方向下的候选问题。受搜索和推荐系统的启发，我们构建了Find、Attempt and Recommend（FAR），这是一个文献评审级联流程，可自动搜索合适的问题，并将人类注意力聚焦于经过多轮筛选的成果上。在一项组合数学试点研究中，该流程从5245篇组合数学论文入手，恢复出6453个候选猜想或未解决问题，并将其筛选为4717个表述清晰且仍未解决的猜想。后续的推理和自动分类阶段呈现出598个潜在解决方案，并选出77个项目供作者团队评审。其中，我们发现了许多有趣的成果，包括关于Davies-Jenssen-Perkins-Roberts、Erdős-Straus、Ikenmeyer-Pak-Panova以及Lund-Saraf-Wolf等猜想和问题的结果。这些成果证明了这种新型人机协作模式在数学发现中的有效性。
英文摘要
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.
发表机构
- Carnegie Mellon University（卡内基梅隆大学）
- Anysphere Co.（Anysphere公司）
机构由 AI 辅助整理，请以论文原文为准。
