用范畴论案例测试大模型，探索AI如何辅助数学研究
In between myth and reality: AI for math -- a case study in category theory
- 以范畴论为实验场景，对比分析两大主流AI系统表现
- 发现当前AI在复杂数学推理中仍存显著局限
- 为开发者提供改进方向，助力AI更深入参与科研
近年来，人们对AI解决数学问题的能力日益关注，已开展多项测试，结果各异。本文通过一项实验，探讨了两个最具代表性的当代AI系统在数学研究方向的表现。实验旨在理解AI如何辅助数学研究，并为AI系统开发者提供改进建议。研究聚焦于范畴论这一高度抽象的数学领域，评估AI在概念构建、证明生成与形式化表达方面的能力，揭示其在复杂逻辑推演中的优势与瓶颈。实验结果表明，尽管部分推理任务可由AI完成，但在创造性建模与深层结构理解上仍远未达到人类研究者水平。本研究为未来AI辅助数学研究提供了实证依据和具体优化路径。
原文摘要 · Abstract (English)
Recently, there is an increasing interest in understanding the performance of AI systems in solving math problems. A multitude of tests have been performed, with mixed conclusions. In this paper we discuss an experiment we have made in the direction of mathematical research, with two of the most prominent contemporary AI systems. One of the objective of this experiment is to get an understanding of how AI systems can assist mathematical research. Another objective is to support the AI systems developers by formulating suggestions for directions of improvement.
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