发表机构
University of Edinburgh; University of Manchester（爱丁堡大学; 曼彻斯特大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究比较AI与人类在11个数学问题上的研究记录，发现AI侧重解决问题和跨领域整合，而人类更注重方法阐述与局限说明，揭示两种不同的研究特征。
AI 中文摘要
AI系统已经开始在长期未解的数学问题上报告解决方案、反例和实质性进展，这引发了关于它们是否以与数学家相同的方式进行研究的疑问。本研究将公开的AI研究记录与人类文献在11个此类问题上进行了比较。人类语料库包含58篇直接针对相同数学目标（这些目标后来被AI来源报告为已解决、已反驳或已取得实质性进展）的论文；从这些材料中构建了31项问题内比较。六项经过验证的基于文本的测量指标捕捉了问题解决程度、方法阐述、不确定性与边界说明、后续问题生成、通用性以及跨学科整合。AI记录更侧重于解决焦点问题和跨领域连接思想。人类论文则显著更多地关注解释方法、明确假设与局限性，以及识别后续研究的问题。在通用性方面未检测到精确差异。当逐一移除每个数学问题时，估计的方向保持不变。研究结果揭示了两种截然不同的研究特征：AI记录集中于闭合和重组问题，而数学论文则更广泛地记录了程序、局限和研究机会，通过这些，结果成为累积知识。因此，评估研究型AI需要关注探究的组织方式，而不仅仅是目标是否被解决。
英文摘要
AI systems have begun to report solutions, disproofs, and substantive advances on long-standing mathematical problems, raising questions about whether they approach research in the same way as mathematicians. This study compares public AI research accounts with the human literature on 11 such problems. The human corpus contains 58 papers that directly addressed the same mathematical targets later reported by AI sources as resolved, disproved, or substantially advanced; 31 within-problem comparisons were constructed from these materials. Six validated text-based measures capture problem resolution, method articulation, uncertainty and boundary specification, successor-question generation, generality, and cross-disciplinary integration. AI accounts place greater emphasis on resolving the focal problem and connecting ideas across fields. Human papers devote significantly more attention to explaining methods, specifying assumptions and limitations, and identifying questions for subsequent research. No precise difference is detected in generality. The estimated directions remain unchanged when each mathematical problem is removed in turn. The findings reveal two distinct research profiles: AI accounts concentrate on closing and recombining problems, whereas mathematical papers more extensively document the procedures, limits, and research opportunities through which results become cumulative knowledge. Evaluating research AI therefore requires attention to the organization of inquiry, not only whether a target is solved.
