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  "title": {
    "zh": "AI用11天证明费马大定理，写下史上最长数学证明",
    "en": "AI Just Solved a 350-Year-Old Math Problem By Writing the Longest Proof Ever"
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    "zh": "Anthropic宣布，其Claude AI仅用11天便独立完成了费马大定理的形式化证明，生成了约1300万行可逐行机器验证的代码。该证明经数学家Kevin Buzzard验证成立，据称是史上最长的数学证明，并且赶超了伦敦帝国理工学院一个尚未完成的人工项目。\n\n这标志着AI驱动形式化验证的突破，表明AI能够独立完成即使是人类团队仍在努力推进的重大定理形式化工作。它可能改变数学家验证证明的方式，并加速AI作为数学与计算机科学研究助手的应用。\n\n该工作使用了数十个Claude智能体并行工作，并借助彭天一（Tianyi Peng）团队在哥伦比亚大学开发的协作工具Prove2Me，通过实时待办列表协调各智能体。最终证明中约有7%的行来自早期的错误尝试；形式化过程使用Lean证明助手语言，使计算机能够逐行验证。",
    "en": "Anthropic's Claude AI independently produced the longest formal proof ever, solving Fermat's Last Theorem in 11 days, a feat that a human-led project has not yet completed."
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      "title_zh": "AI用11天证明费马大定理，写下史上最长数学证明",
      "title_en": "AI Just Solved a 350-Year-Old Math Problem By Writing the Longest Proof Ever",
      "what_changed_zh": "Anthropic宣布，其Claude AI仅用11天便独立完成了费马大定理的形式化证明，生成了约1300万行可逐行机器验证的代码。该证明经数学家Kevin Buzzard验证成立，据称是史上最长的数学证明，并且赶超了伦敦帝国理工学院一个尚未完成的人工项目。\n\n这标志着AI驱动形式化验证的突破，表明AI能够独立完成即使是人类团队仍在努力推进的重大定理形式化工作。它可能改变数学家验证证明的方式，并加速AI作为数学与计算机科学研究助手的应用。\n\n该工作使用了数十个Claude智能体并行工作，并借助彭天一（Tianyi Peng）团队在哥伦比亚大学开发的协作工具Prove2Me，通过实时待办列表协调各智能体。最终证明中约有7%的行来自早期的错误尝试；形式化过程使用Lean证明助手语言，使计算机能够逐行验证。",
      "what_changed_en": "Anthropic's Claude AI independently produced the longest formal proof ever, solving Fermat's Last Theorem in 11 days, a feat that a human-led project has not yet completed.",
      "current_state_zh": "Anthropic宣布，其Claude AI仅用11天便独立完成了费马大定理的形式化证明，生成了约1300万行可逐行机器验证的代码。该证明经数学家Kevin Buzzard验证成立，据称是史上最长的数学证明，并且赶超了伦敦帝国理工学院一个尚未完成的人工项目。\n\n这标志着AI驱动形式化验证的突破，表明AI能够独立完成即使是人类团队仍在努力推进的重大定理形式化工作。它可能改变数学家验证证明的方式，并加速AI作为数学与计算机科学研究助手的应用。\n\n该工作使用了数十个Claude智能体并行工作，并借助彭天一（Tianyi Peng）团队在哥伦比亚大学开发的协作工具Prove2Me，通过实时待办列表协调各智能体。最终证明中约有7%的行来自早期的错误尝试；形式化过程使用Lean证明助手语言，使计算机能够逐行验证。",
      "current_state_en": "Anthropic's Claude AI independently produced the longest formal proof ever, solving Fermat's Last Theorem in 11 days, a feat that a human-led project has not yet completed.",
      "detailed_summary_zh": "Anthropic's Claude AI independently produced the longest formal proof ever, solving Fermat's Last Theorem in 11 days, a feat that a human-led project has not yet completed.",
      "detailed_summary_en": "Anthropic's Claude AI independently produced the longest formal proof ever, solving Fermat's Last Theorem in 11 days, a feat that a human-led project has not yet completed.",
      "background_zh": "费马大定理的内容是：不存在正整数a、b、c，使得对于大于2的整数n有a^n + b^n = c^n。法国数学家皮埃尔·德·费马约在1637年将这一论断写在书页边缘，并称自己有一个‘绝妙的证明’，只是空白处写不下；直到1995年安德鲁·怀尔斯发表了129页的证明，才最终解决这一猜想。形式化证明是指将数学推理转换成Lean等计算机可核验的形式语言，使每个逻辑步骤都能由机器检查。",
      "background_en": "Fermat's Last Theorem states that for integers greater than 2, no three positive integers a, b, and c can satisfy a^n + b^n = c^n. French mathematician Pierre de Fermat wrote the claim in a book margin around 1637 and said he had a proof too large to fit; it took Andrew Wiles's 129-page proof, published in 1995, to resolve the conjecture. Formalizing a proof means translating mathematical reasoning into a machine-checkable formal language such as Lean, so that every logical step can be verified by a computer.",
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      "importance_score": 8.5,
      "references": [
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          "url": "https://en.wikipedia.org/wiki/Fermat's_Last_Theorem",
          "title": "Fermat's Last Theorem"
        },
        {
          "url": "https://www.anthropic.com/research/formalizing-fermats-last-theorem",
          "title": "Formalizing Fermat's Last Theorem \\ Anthropic"
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          "url": "https://en.wikipedia.org/wiki/Formal_proof",
          "title": "Formal proof - Wikipedia"
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