AI and Human Approaches to Mathematical Problem Solving

2026-09-15

AI Summary

该研究通过比较AI和人类在解决11个数学问题上的方法，发现AI更侧重于解决问题和跨领域连接，而人类则更注重方法解释、假设限定及后续研究问题的提出。

Abstract

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.

Problem

• AI systems
• mathematical problem solving
• research methods
• human mathematicians
• problem resolution

Innovation

• problem solving
• method articulation
• cross-disciplinary integration
• research profile comparison