Xiaokai Li

Three large language models independently reproved all 465 propositions of Euclid's Elements, and their citation choices differ systematically from Heath's human-proof baseline. Mean pairwise Jaccard similarity among three Claude Opus 4.6 runs is 0.68, nearly twice the 0.37 between AI and human proofs, so the difference is stable and reproducible. Its concrete signature is that about 40% of AI citations point to foundational elements such as definitions, common notions and postulates, against only 13% in human proofs.

Three large language models independently reproved all 465 propositions of Euclid's Elements, and their citation choices differ systematically from Heath's human-proof baseline. Mean pairwise Jaccard similarity among three Claude Opus 4.6 runs is 0.68, nearly twice the 0.37 between AI and human proofs, so the difference is stable and reproducible. Its concrete signature is that about 40% of AI citations point to foundational elements such as definitions, common notions and postulates, against only 13% in human proofs.