Anthropic 旗下 Claude 完成费马大定理的首个 Lean 机器形式化证明
Anthropic 宣布 Claude 利用交互式证明助手 Lean 4 完成了费马大定理的首个全机器验证形式化证明，生成了超 1300 万行经检验的代码。
Anthropic 宣布其大语言模型 Claude 成功利用 Lean 4 交互式定理证明器，完成了费马大定理的首个完全机器可验证的形式化证明。这项成果将英国数学家安德鲁·怀尔斯（Andrew Wiles）于 1995 年发表的著名证明转换为了计算机能够逐行严格核对的形式系统语言。
该形式化工程被认为是目前规模最大的 Lean 证明代码库，总计包含超过 1300 万行代码。为了支撑整个核心论证，该项目同时形式化并验证了超过 2.9 万个此前未被数字化的辅助定理与数学定义，涵盖了数论与代数几何等多个深奥领域。
数学界此前普遍预计此类超大规模的形式化工作需要数学家团队耗时数年甚至数十年才能完成。Claude 成功落地该证明，标志着人工智能在形式化推理、数学验证以及自动化软硬件安全验证领域迈出了关键一步。
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by Editorial Team Share Add us on Google Pierre de Fermat scribbled a note in the margin of a math textbook in 1637, claiming he had a proof that was too large to fit in the space. It took 358 years for a human to actually prove him right. Now an AI has done something arguably harder: translating that proof into language a computer can verify, line by line, with zero ambiguity. Anthropic’s Claude has produced the first complete machine-checked formalization of Fermat’s Last Theorem using Lean 4, a proof assistant that functions like a brutally honest math teacher who refuses to let you skip any steps. The formalization covers over 29,511 theorems and 1,450 definitions, all verified through Lean’s kernel without relying on axioms outside the standard Mathlib foundations. [...] Share Add us on Google by Editorial Team Pierre de Fermat scribbled a note in the margin of a math textbook in 1637, claiming he had a proof that was too large to fit in the space. It took 358 years for
"Checking that a major mathematical proof is correct can take years. Formalization — converting the mathematical reasoning into a form computer proof assistants like Lean can verify — can help. Last month, Claude completed the first formalized proof of Fermat's Last Theorem, one of the most famous theorems of all time. This was a project experts thought would take many years. It is the largest Lean proof ever written. Fermat's Last Theorem was first proven in 1995 by Sir Andrew Wiles, more than 350 years after it was conjectured. Our proof, which totals over 13 million lines of code, provides machine verification. More importantly, it proves over 29,000 other theorems that the proof requires, across many areas of math which had never before been formalized. We see this as a major step in [...] On September 5, 2026, Anthropic announced that Claude had completed the first fully formalized, machine-checked Lean 4 proof of Fermat's Last Theorem — a project the company says experts thought
Formalizing a proof means translating it into a language so painfully literal that a computer can verify every step on its own without entering into subjectivities. Mathematicians have been bad at policing this for a while. A 1908 German prize worth roughly $1 million to $2 million in today's money, offered for the first valid proof of the theorem, drew 621 wrong submissions in its first year alone. Checking that a major mathematical proof is correct can take years. Formalization—converting the mathematical reasoning into a form computer proof assistants like Lean can verify—can help. Last month, Claude completed the first formalized proof of Fermat's Last Theorem, one of… pic.twitter.com/pdT8zwlV4A — Anthropic (@AnthropicAI) September 4, 2026
## Alexander Kruel's Post ### Alexander Kruel 3h · Anthropic: "Checking that a major mathematical proof is correct can take years. Formalization—converting the mathematical reasoning into a form computer proof assistants like Lean can verify—can help. Last month, Claude completed the first formalized proof of Fermat’s Last Theorem, one of the most famous theorems of all time. This was a project experts thought would take many years. It is the largest Lean proof ever written.
Checking that a major mathematical proof is correct can take years. Formalization—converting the mathematical reasoning into a form computer proof assistants like Lean can verify—can help. Last month, Claude completed the first formalized proof of Fermat’s Last Theorem, one of the most famous theorems of all time. This was a project experts thought would take many years. It is the largest Lean proof ever written. Fermat’s Last Theorem was first proven in 1995 by Sir Andrew Wiles, more than 350 years after it was conjectured. Our proof, which totals over 13 million lines of code, provides machine verification. More importantly, it proves over 29,000 other theorems that the proof requires, across many areas of math which had never before been formalized. We see this as a major step in the [...] Checking that a major mathematical proof is correct can take years. Formalization—converting the mathematical reasoning into a form computer proof assistants like Lean can verify—can help. Last mo
Checking that a major mathematical proof is correct can take years. Formalization—converting the mathematical reasoning into a form computer