← 研踪 PaperTrailarXiv:2611.16527 · v1
AI has its own style in mathematical proving
首次提交 2026-11-12 17:27
版本更新 2026-11-12 17:27
雷达观测 2026-11-13 14:15
摘要
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.
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v1 · 2026-11-12 17:27 · 最新观测版本
AI has its own style in mathematical proving
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.
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