AI 证明数学题有自己独特的风格：从基础公理重新搭起论证
AI has its own style in mathematical proving
AI 导读
一项研究让三个大语言模型独立重新证明《几何原本》全部 465 个命题，并与人类证明的引用结构对比。结果显示 AI 证明的引用风格与人类明显不同且可复现：AI 之间两两 Jaccard 相似度约 0.68，几乎是 AI 与人类之间（约 0.37）的两倍；约 40% 的 AI 引用指向定义、公设等基础元素，人类仅为 13%。研究者将这种从基础出发而非直接引用已有定理的风格称为“从零搭建”。
正文 · 原文
Abstract:As large language models increasingly generate mathematical proofs, whether they develop a proving style distinct from that of human mathematicians remains an open question. This question is particularly pressing as mathematicians increasingly voice concerns that proofs generated by large language models are difficult to interpret. Here we ask three large language models to independently reprove all 465 propositions of Euclid's \textit{Elements} and compare their citation choices against the human-proof baseline through Jaccard similarity and complex network analysis. We find that AI-generated proofs differ from human proofs, and this difference is stable and reproducible: mean pairwise Jaccard similarity among AI runs (~0.68) is nearly twice that between AI and human proofs (~0.37), and cross-run classification consistency is also high. By examining citation structure in detail, we identify the concrete signature of this difference: approximately 40% of AI citations point to foundational elements (definitions, common notions, and postulates), compared with only 13\% in human proofs; even among theorem-to-theorem citations, AI tends to cite more distant results. Roughly half of AI's extra citations trace to the upstream dependencies of the human proof. Together, these findings suggest that the AI proving style is a tendency to construct arguments on its own from foundational elements rather than directly citing later, more established results, which we term "building from the ground up". Our findings offer a new perspective on how AI systems organise and invoke mathematical knowledge, with implications for understanding the interpretability of AI-generated proofs.
| Subjects: | Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2611.16527 [cs.AI] |
| (or arXiv:2611.16527v1 [cs.AI] for this version) | |
| https://doi.org/10.48550/arXiv.2611.16527 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Xiaokai Li [view email]
[v1]
Thu, 12 Nov 2026 09:27:02 UTC (828 KB)
来源：arXiv cs.AI · arxiv.org