{"@context":"https://schema.org","@type":"NewsArticle","generatedAt":"2026-10-31T11:00:49.146Z","headline":"Claude 用 11 天完成费马大定理的首个完整机器验证证明","description":"Anthropic 发布首个完整机器验证的费马大定理证明，Claude 在 11 天内基本自主完成，写出 1300 万行 Lean 代码并证明 29，500 个中间定理。","url":"https://www.aioga.com/news/cmtnapudv01zbrog16o6dxgoi/","mainEntityOfPage":"https://www.aioga.com/news/cmtnapudv01zbrog16o6dxgoi/","datePublished":"2026-09-03T16:00:00.000Z","dateModified":"2026-09-03T16:00:00.000Z","inLanguage":"zh-CN","publisher":{"@type":"NewsMediaOrganization","name":"Aioga","url":"https://www.aioga.com"},"citation":["https://www.anthropic.com/research/formalizing-fermats-last-theorem","https://aihot.virxact.com/items/cmtnapudv01zbrog16o6dxgoi"],"canonicalUrl":"https://www.aioga.com/news/cmtnapudv01zbrog16o6dxgoi/","directAnswer":{"@type":"Answer","text":"Anthropic 发布了首个完整的计算机验证费马大定理证明。其材料称，Claude 在 11 天内基本自主完成形式化工作，使用 Lean 编写约 1300 万行代码，并证明 29,500 个中间定理。","url":"https://www.aioga.com/news/cmtnapudv01zbrog16o6dxgoi/","dateCreated":"2026-09-03T16:00:00.000Z","author":{"@type":"Organization","@id":"https://www.aioga.com/authors/aioga-editorial/#editorial-team","name":"Aioga Editorial Team","url":"https://www.aioga.com/authors/aioga-editorial/"}},"evidence":[{"@type":"CreativeWork","name":"Anthropic source article","url":"https://www.anthropic.com/research/formalizing-fermats-last-theorem","datePublished":"2026-09-03T16:00:00.000Z","provider":{"@type":"Organization","name":"Anthropic","url":"https://www.anthropic.com/research/formalizing-fermats-last-theorem"}},{"@type":"CreativeWork","name":"AIHot archive record","url":"https://aihot.virxact.com/items/cmtnapudv01zbrog16o6dxgoi","datePublished":"2026-09-03T16:00:00.000Z","provider":{"@type":"Organization","name":"AIHot","url":"https://aihot.virxact.com/items/cmtnapudv01zbrog16o6dxgoi"}}],"aggregationSource":"Anthropic：Research（发表成果 · 网页）","originalPublisher":{"name":"Anthropic","url":"https://www.anthropic.com/research/formalizing-fermats-last-theorem"},"geoDeepAnswer":null,"article":{"id":"cmtnapudv01zbrog16o6dxgoi","slug":"cmtnapudv01zbrog16o6dxgoi","url":"https://www.aioga.com/news/cmtnapudv01zbrog16o6dxgoi/","title":"Claude 用 11 天完成费马大定理的首个完整机器验证证明","title_en":"","summary":"Anthropic 发布首个完整机器验证的费马大定理证明，Claude 在 11 天内基本自主完成，写出 1300 万行 Lean 代码并证明 29，500 个中间定理。","source":"Anthropic：Research（发表成果 · 网页）","sourceUrl":"https://www.anthropic.com/research/formalizing-fermats-last-theorem","aiHotUrl":"https://aihot.virxact.com/items/cmtnapudv01zbrog16o6dxgoi","publishedAt":"2026-09-03T16:00:00.000Z","category":"行业动态","score":72,"selected":true,"articleBody":["We are sharing the first complete computer-checked proof of Fermat’s Last Theorem. Claude worked largely autonomously over 11 days to write the proof in the Lean programming language. Below, we describe how the formalization was done and share some thoughts about what this work could mean for research mathematics. Around 1637, Pierre de Fermat jotted down a claim in the margin of his copy of Diophantus’s Arithmetica that would become one of the most famous mathematical conjectures of all time: no positive integers a, b, c satisfy aⁿ + bⁿ = cⁿ for any n > 2. Fermat’s Last Theorem：https://www.youtube.com/watch?v=1BSFyEIY2BY (FLT), as the conjecture became known, turned out to be incredibly difficult to prove. The first proof, from Sir Andrew Wiles in 1995, ran to 129 pages and required months of painstaking work to verify.","A decade later, Dutch computer scientist Jan Bergstra proposed “formalizing” Wiles’s proof: converting the mathematical reasoning into a form computers can check automatically. Since then, mathematicians have been developing the methods needed to encode such a complex proof, including a multi-year community effort kicked off in 2024 by Kevin Buzzard at Imperial College London to complete the formalization：https://lean-lang.org/use-cases/flt/ using the Lean proof assistant：https://en.wikipedia.org/wiki/Lean_(proof_assistant).","Recently, Tianyi Peng, an Anthropic researcher whose group at Columbia University builds tools for AI formalization, set out to test whether Claude could make progress on formalizing FLT. 1 The result went further than he expected. In 11 days, working largely autonomously, Claude produced the first end-to-end, computer-checked proof of FLT. Along the way, it wrote 13 million lines of Lean and proved 29,500 intermediate theorems.","We shared the resulting proof：https://github.com/anthropics/fermats-last-theorem with Kevin Buzzard, who said:","Automatically formalizing a proof as complex as FLT is a significant step towards a future in which all of mathematics can be readily checked. As AI produces ever more proofs, the ability to easily formalize work can lighten the burden of evaluating new results (a process that can take years). We are hopeful that it will become easier, not harder, to trust the body of knowledge upon which mathematics is built.","Unlike recent AI-driven：https://www.anthropic.com/research/riemann-zeta work on the Riemann hypothesis, which produced novel mathematics , what’s novel here is the verification —checking a mathematical proof as one would check a mathematical computation with a calculator. Proving math theorems requires assembling complex logical chains, and if a single link is broken, everything that follows it might turn out to be false. Understanding a novel result deeply enough to be confident in its correctness can take months, or even years, of work.","Fermat’s Last Theorem is an illustrative example. 2 Fermat wrote down the theorem’s statement in the margin of a book, alongside a tantalizing note:","For over 350 years, generations of mathematicians searched for a proof of FLT, marvelous or otherwise. In 1908, a prize of 100,000 German gold marks (the equivalent of 1–2 million dollars today) was announced for anyone who could produce a correct proof, and 621 incorrect attempts were produced in the first year alone.","In June 1993, Wiles presented what he believed to be the first correct proof of FLT in a three-day series of lectures. Two months into an intensive verification effort by several mathematicians, a reviewer asked Wiles a question that exposed a critical gap. Wiles spent a year trying to fix it, first alone and then with his former student Richard Taylor. He was on the brink of abandoning the project when he finally realized an approach he’d discarded earlier could fix the proof. Wiles published the first correct proof of FLT in May 1995; it relied on modern mathematical techniques that were far beyond what would have been known to Fermat in 1637. Since an elementary proof has not been found after centuries of trying, the mathematical community now believes Fermat’s own original “marvelous proof” was incorrect：https://mathenchant.wordpress.com/2016/05/16/fermats-last-theorem-the-curious-incident-of-the-boasting-frenchman/.","One way to check a proof’s correctness is to ask a computer to do it. Proof assistants like Lean verify the logic of a proof algorithmically, demonstrating its correctness beyond a doubt. The difficult part for humans is rewriting the proof so Lean can understand it. While a proof written for human readers will skip many obvious steps, Lean needs to see every step, no matter how trivial. Human proofs also build on centuries of published work, while a formalization starts from the tiny fraction of math that’s been formalized already.","For FLT, the formalization process was expected to take years. Just the blueprint：https://imperialcollegelondon.github.io/FLT/blueprint.pdf the mathematical community has been using to describe the initial phase of the project runs to 86 pages.","Claude completed the proof in 11 days, producing computer-verifiable proofs of 30,300 theorems along the way (using 29,500 in the final proof). Dozens of Claude agents collaborated to define concepts, prove intermediate theorems, and use those theorems to prove ever harder statements. At 13 million lines of Lean code, Claude’s proof is over 5x the size of Mathlib, the principal community library of mathematical proofs this theorem builds on. 3","Claude’s proof follows a simplified version of Wiles’s proof from Darmon, Diamond and Taylor：https://www.math.mcgill.ca/darmon/pub/Articles/Expository/05.DDT/paper.pdf. Mathematical input from humans was limited to occasional high-level instructions from Tianyi: “Jacobian as a scheme sounds high priority,” “push [the] Mazur [theorem] to be done soon.” You can find excerpts of Claude’s thinking here：https://www-cdn.anthropic.com/9e431dff043da6538d99d6c2d231b670aa3da263.pdf.","Excerpts of Claude’s thinking as it realizes what it has just accomplished.","A number of Claude’s initial attempts failed: while agents had some early success, they quickly lost track of the project’s state and stopped collaborating effectively. Their failed efforts contributed ~7% of the non-boilerplate lines in the final proof.","The effort succeeded when we switched to using Prove2Me：https://prove2me.vercel.app/, an open collaborative platform for formalizing mathematics designed by Tianyi Peng and his collaborators at Columbia University. Prove2Me helped by:","With Prove2Me and a Claude Code-based multi-agent harness, a team of agents completed the proof in a little under two weeks, consuming about six billion output tokens from a general-purpose internal research model roughly comparable to Claude Fable 5.1. The finished proof was checked by Lean; it uses just Lean’s three standard axioms, and a comparator：https://github.com/leanprover/comparator confirmed that the theorem’s statement matches Mathlib’s own statement of FLT.","The speed with which we were able to produce this proof demonstrates that it is now possible to formalize large swaths of mathematics, which may both catch errors in the common body of mathematical proofs and reduce the burden of refereeing new work. After reviewing Claude’s Lean proof, Kevin Buzzard told us:","Formalization is also a major factor in how humans can gain confidence in AI-generated mathematical results. As AI and AI-assisted mathematicians produce more (purported) proofs than ever before, AI-assisted formalization takes part of the load off human reviewers. We expect it will become common to produce a formalized proof alongside any write-up intended for a human reader. Although we do not think a formalized proof should replace a human-understandable exposition, it may be the only feasible way for the mathematical community to keep up with AI-generated contributions.","Writing Lean also seems to help Claude prove novel results. Many of our recent Claude-authored results have been formalized in parallel with their proofs, and Claude appears to use these partial proofs to independently check its hypotheses much like it writes numerical simulations to check that it’s on the right track.","Formalizing FLT was a token-intensive project, but it is also the largest Lean proof ever constructed. Anthropic researchers did a small experiment using three personal Claude Max plans to formalize applications of the Hardy-Littlewood Circle Method. Collaborating entirely through Prove2Me, the agents jointly completed a formalization of Vinogradov’s Three Primes Theorem：https://en.wikipedia.org/wiki/Vinogradov%27s_theorem in just three days. We think with the right scaffold, collaborative formalization of major results with consumer AI subscriptions is achievable.","To this end, Anthropic：https://www.anthropic.com/news/expanding-support-for-scientists as well as other labs：https://openai.com/index/chatgpt-for-academic-researchers/ have recently expanded their support for external researchers—including mathematicians working on pure math and formalization—with free and discounted subscriptions and research credits. We also offer dedicated grants：https://www.anthropic.com/news/ai-for-science-program for larger scientific projects, which could include formalizing other major theorems or improving Lean or Mathlib.","With AI rapidly changing what it looks like to do math research, mathematicians—at Anthropic and elsewhere—are grappling with what that means for their work：https://leidendeclaration.ai/. Formalization, however, is a place where we feel unambiguously good about the role of AI. As formalization becomes a more commonplace tool, we are hopeful that it will help maintain trust in the common body of mathematical knowledge.","Our formalization effort is a small piece of the long history of Fermat’s theorem and the development of formal mathematics. The first full proof from Andrew Wiles together with Richard Taylor was a culmination of more than three hundred years of mathematics, integrating ideas from Gerhard Frey, Jean-Pierre Serre, Ken Ribet, Barry Mazur, Robert Langlands, Jerrold Tunnell, Yutaka Taniyama, Goro Shimura, and André Weil, among others. Claude’s proof follows the exposition by Henri Darmon, Fred Diamond, and Richard Taylor.：https://www.math.mcgill.ca/darmon/pub/Articles/Expository/05.DDT/paper.pdf","Our proof adapts pieces from the Imperial College London FLT project：https://github.com/ImperialCollegeLondon/FLT led by Kevin Buzzard and the flt-regular project：https://github.com/leanprover-community/flt-regular. Lean and Mathlib are both their own labors of love and have received contributions from hundreds of mathematicians, many working with the Lean FRO：https://lean-lang.org/fro/. We thank Kevin Buzzard for reviewing the proof and for his comments.","The full proof is available on GitHub：https://github.com/anthropics/fermats-last-theorem along with a written walk-through of the proof.","We had Claude autonomously train models to improve their performance on several public benchmarks that measure 10 categories of alignment failure. For all 10, Claude found fixes that improved the target benchmarks without degrading capabilities.","In this post, we share two results that show how Claude can help life scientists increase the pace of their research.","Features on AI-assisted discoveries, practical workflows, and field notes across the sciences."],"articleImages":[{"sourceUrl":"https://www.anthropic.com/_next/image?url=https%3A%2F%2Fwww-cdn.anthropic.com%2Fimages%2F4zrzovbb%2Fwebsite%2F578f91575c42231f0994e341014614255149af80-1200x630.jpg&w=3840&q=75","alt":"Formalizing Fermat's Last Theorem","afterParagraph":0,"url":"/media/articles/cmtnapudv01zbrog16o6dxgoi/3bf50bf7a711dcf3.webp"},{"sourceUrl":"https://www.anthropic.com/_next/image?url=https%3A%2F%2Fwww-cdn.anthropic.com%2Fimages%2F4zrzovbb%2Fwebsite%2Fafd8e238255ec2654f2322f3d3630dcf1e8ea4ca-6800x3264.png&w=3840&q=75","alt":"DAG showing Claude formalizing sub-theorems on the way to FLT","afterParagraph":15,"url":"/media/articles/cmtnapudv01zbrog16o6dxgoi/16acfe50d3100648.webp"}],"mediaStatus":"ok","articleBodyZh":["我们分享费马大定理的首个完整的计算机检查证明。克洛德在11天内几乎自主地用精益编程语言编写了证明。下面，我们将描述形式化过程，并分享对这项工作对数学研究可能带来的影响的一些想法。大约在1637年，皮埃尔·德·费马在他著的《丢番图算术》边注记下了一个主张，这成为史上最著名的数学猜想之一：对于任意n>2，没有正整数a、b、c满足aⁿ + bⁿ = cⁿ。费马大定理：https：//www.youtube.com/watch？v=1BSFyEIY2BY（FLT），这一猜想证明极其困难。1995年安德鲁·怀尔斯爵士提出的第一个证明长达129页，经过数月的艰苦验证。","十年后，荷兰计算机科学家Jan Bergstra提出了“形式化”怀尔斯证明：将数学推理转化为计算机能自动检查的形式。从那时起，数学家们一直在开发编码如此复杂证明的方法，包括2024年由帝国理工学院的Kevin Buzzard发起的多年社区努力，利用精益证明Lean_助手完成了形式化：https：//lean-lang.org/use-cases/flt/（proof_assistant）。","最近，哥伦比亚大学人类学研究员彭天一，其团队致力于构建人工智能形式化工具，着手测试克劳德是否能取得FLT形式化的进展。结果超出了他的预期。在11天内，克劳德几乎自主地完成了FLT的首个端到端、计算机检查证明。在此过程中，他编写了1300万行精益理论，并证明了29500条中间定理。","我们将所得的证明分享给了 Kevin Buzzard，他说：","自动形式化像FLT这样复杂的证明，是迈向未来数学都能被轻松检验的重要一步。随着人工智能产生越来越多的证明，能够轻松形式化工作，可以减轻评估新结果（这一过程可能需要数年）。我们希望，信任构成数学的知识体系会变得更容易，而非更困难。","不同于最近由人工智能驱动的关于黎曼假设的工作（例如：https://www.anthropic.com/research/riemann-zeta），这些工作产生了新的数学内容，这里的新颖之处在于验证——像使用计算器检查数学计算一样检查数学证明。证明数学定理需要组装复杂的逻辑链，如果其中任何一个环节出错，之后的所有内容都可能是错误的。深入理解一个新的结果并对其正确性有信心，可能需要数月甚至数年的工作。","费马大定理是一个说明性的例子。费马在一本书的页边写下了定理的陈述，并附上一条引人注意的说明：","350 多年来，一代又一代的数学家都在寻找费马大定理的证明，无论是惊人的还是常规的。1908年，为了奖励任何能提出正确证明的人，宣布了10万德国金马克的奖金（相当于今天的100万到200万美元），仅在第一年就产生了621个不正确的尝试。","1993年6月，韦尔斯在为期三天的系列讲座中展示了他认为是第一份正确的费马大定理证明。在几位数学家进行的密集验证工作两个月后，一位审稿人向韦尔斯提出了一个问题，暴露了关键的漏洞。韦尔斯花了一年时间尝试修复，先是独自一人，然后与他的前学生理查德·泰勒合作。当他几乎要放弃这个项目时，他最终意识到自己早先放弃的一种方法可以修复证明。韦尔斯于1995年5月发表了费马大定理的第一份正确证明；该证明依赖于现代数学技术，这些技术远超费马在1637年所知。由于经过数百年的努力仍未找到初等证明，数学界现在认为费马自称的“惊人证明”实际上是不正确的：https://mathenchant.wordpress.com/2016/05/16/fermats-last-theorem-the-curious-incident-of-the-boasting-frenchman/。","检查证明正确性的一种方法是让计算机来做。像 Lean 这样的证明助手可以算法化地验证证明的逻辑，毫无疑问地展示其正确性。对于人类来说，困难的部分是改写证明以便 Lean 能理解。为人类读者编写的证明会跳过许多显而易见的步骤，而 Lean 需要看到每一步，无论多么微不足道。人类的证明也建立在数个世纪的已发表工作之上，而形式化证明则是从已经形式化的数学的一小部分开始。","对于费马大定理（FLT），形式化过程预计将耗费数年时间。仅仅是蓝图：https://imperialcollegelondon.github.io/FLT/blueprint.pdf 数学界用来描述项目初期阶段就有 86 页。","Claude 在 11 天内完成了证明，在此过程中产生了 30,300 个计算机可验证的定理（最终证明中使用了 29,500 个）。数十个 Claude 代理协作定义概念、证明中间定理，并使用这些定理去证明更难的命题。Claude 的证明有 1,300 万行 Lean 代码，其规模超过 Mathlib 的 5 倍，Mathlib 是该定理所依赖的主要社区数学证明库。3","Claude 的证明遵循 Darmon、Diamond 和 Taylor 的 Wiles 证明的简化版本：https://www.math.mcgill.ca/darmon/pub/Articles/Expository/05.DDT/paper.pdf。人类数学输入仅限于 Tianyi 的偶尔高级指令：“Jacobian 作为一个 scheme 看起来优先级很高”，“尽快完成 [Mazur 定理]”。你可以在这里找到 Claude 思考的摘录：https://www-cdn.anthropic.com/9e431dff043da6538d99d6c2d231b670aa3da263.pdf。","Claude 在意识到自己刚刚完成的成果时的思考摘录。","Claude 的最初尝试中有若干失败：尽管代理早期取得了一些成功，但他们很快失去了对项目状态的跟踪，停止了有效协作。他们失败的尝试贡献了最终证明中约 7% 的非模板化代码行。","当我们转向使用 Prove2Me：https://prove2me.vercel.app/ 时，这项工作得以成功，这是一种由 Tianyi Peng 及其哥伦比亚大学的合作团队设计的开放协作数学形式化平台。Prove2Me 通过以下方式提供了帮助：","通过 Prove2Me 和基于 Claude Code 的多智能体系统，一个智能体团队在不到两周的时间内完成了证明，消耗了大约六十亿个通用内部研究模型的输出令牌，该模型大致相当于 Claude Fable 5.1。最终的证明经过 Lean 检查；它仅使用 Lean 的三个标准公理，以及一个比较器：https://github.com/leanprover/comparator，确认定理的陈述与 Mathlib 自身对 FLT 的陈述一致。","我们能够如此快速地生成这一证明表明，现在有可能形式化大量数学，这既可能发现数学已知证明中的错误，也可以减轻审阅新工作的负担。在审查 Claude 的 Lean 证明后，Kevin Buzzard 告诉我们：","形式化也是人类对 AI 生成的数学结果建立信心的一个重要因素。随着 AI 和 AI 辅助数学家产生的（所谓）证明比以往更多，AI 辅助的形式化减轻了人类审阅者的一部分负担。我们预计，在为人类读者准备的任何写作中，同时生成形式化证明将变得普遍。虽然我们认为形式化证明不应取代人类可理解的阐述，但它可能是数学界跟上 AI 生成贡献的唯一可行方法。","编写 Lean 代码似乎也有助于 Claude 证明新颖结果。我们最近许多由 Claude 创作的结果都是在其证明的同时进行形式化的，Claude 似乎利用这些部分证明独立检查其假设，就像它编写数值模拟以确认自己方向正确一样。","形式化 FLT 是一个令牌密集型项目，但它也是迄今为止构建的最大 Lean 证明。Anthropic 的研究人员做了一个小实验，使用三个个人 Claude Max 计划来形式化 Hardy-Littlewood 圆法的应用。完全通过 Prove2Me 协作，智能体们在短短三天内共同完成了 Vinogradov 三素数定理的形式化：https://en.wikipedia.org/wiki/Vinogradov%27s_theorem。我们认为，有了合适的支架，通过消费者 AI 订阅进行重大结果的协作形式化是可实现的。","为此，Anthropic：https://www.anthropic.com/news/expanding-support-for-scientists 以及其他实验室：https://openai.com/index/chatgpt-for-academic-researchers/ 最近扩大了对外部研究人员的支持——包括从事纯数学和形式化研究的数学家——提供免费和折扣订阅以及研究积分。我们还提供专项资助：https://www.anthropic.com/news/ai-for-science-program，用于更大规模的科学项目，这可能包括形式化其他重大定理或改进 Lean 或 Mathlib。","随着 AI 快速改变数学研究的面貌，数学家们——在 Anthropic 及其他地方——正在思考这对他们的工作意味着什么：https://leidendeclaration.ai/。然而，形式化是我们对 AI 作用感到明确肯定的一个领域。随着形式化成为一种更普遍的工具，我们希望它能帮助维护数学知识的共同信任基础。","我们的形式化工作是费马大定理和形式数学发展的悠久历史中的一小部分。Andrew Wiles 与 Richard Taylor 的首次完整证明是三百多年数学工作的顶点，整合了 Gerhard Frey、Jean-Pierre Serre、Ken Ribet、Barry Mazur、Robert Langlands、Jerrold Tunnell、Yutaka Taniyama、Goro Shimura 以及 André Weil 等人的思想。Claude 的证明遵循 Henri Darmon、Fred Diamond 和 Richard Taylor 的阐述：https://www.math.mcgill.ca/darmon/pub/Articles/Expository/05.DDT/paper.pdf。","我们的证明借鉴了 Kevin Buzzard 领导的伦敦帝国学院 FLT 项目：https://github.com/ImperialCollegeLondon/FLT 以及 flt-regular 项目：https://github.com/leanprover-community/flt-regular 的部分成果。Lean 和 Mathlib 本身是各自的心血结晶，得到了数百名数学家的贡献，其中许多人与 Lean FRO：https://lean-lang.org/fro/ 合作。我们感谢 Kevin Buzzard 对证明进行审阅并提出意见。","完整证明以及书面的证明详解可在 GitHub 上获取：https://github.com/anthropics/fermats-last-theorem","我们让 Claude 自主训练模型，以提高它们在几个公共基准测试上对 10 类对齐失败的表现。对于所有 10 类，Claude 都找到了改进的方法，在不降低能力的情况下提升了目标基准的表现。","在本文中，我们分享两个结果，展示 Claude 如何帮助生命科学家加快他们的研究进程。","涉及 AI 辅助发现、实用工作流程以及各科学领域的实地笔记的特性内容。"],"translationStatus":"translated","bodyOrigin":"source-page","editorial":{"summary":"Anthropic 发布了首个完整的计算机验证费马大定理证明。其材料称，Claude 在 11 天内基本自主完成形式化工作，使用 Lean 编写约 1300 万行代码，并证明 29,500 个中间定理。","background":"费马大定理断言，当 n 大于 2 时，不存在满足 aⁿ+bⁿ=cⁿ 的正整数解。Wiles 于 1995 年完成首个证明；此后，数学界持续尝试将相关推理转化为可由 Lean 等工具自动检查的形式。","viewpoint":"Aioga 判断：此次成果的重点不在提出新的费马大定理数学结论，而在于展示 Claude 能够参与复杂证明的形式化与机器验证。其价值仍需结合证明内容和验证过程进一步理解。","implications":"可能影响：若类似形式化工作持续推进，数学证明的检查方式可能发生变化；但单一案例不足以证明所有复杂数学都能自动形式化，也不代表机器验证已经取代数学家的审阅。","nextStep":"后续观察：应关注该 Lean 证明的公开内容、复核过程及社区反馈，并区分自动形式化、证明生成与数学上提出新结果等不同能力。","evidenceRefs":["title","summary","articleBody","source"],"status":"published","aiGenerated":true,"autoApproved":true,"generatedBy":"aioga-editorial:gpt-5.6-sol","reviewedBy":"aioga-editorial-review:gpt-5.6-sol","generatedAt":"2026-09-05T16:22:43.708Z","sourceHash":"62645c9d194f7f55","review":{"approved":true,"groundedness":96,"clarity":93,"duplicationRisk":28,"blockingIssues":[],"notes":["候选内容整体与来源材料一致，事实陈述、观点判断和条件性推测区分清楚。","“Wiles 于 1995 年完成首个证明”与来源表述一致；“数学界持续尝试形式化”也有正文中相关历史背景支持。","“其价值仍需结合证明内容和验证过程进一步理解”属于审慎性判断，不构成无来源事实断言。"]},"validation":{"passed":true,"mode":"ai-auto","revisions":0,"checks":["schema","length","source-attribution","editorial-labels","inference-boundary","low-source-overlap","no-html","independent-ai-review"]}},"tags":["行业动态","Anthropic：Research（发表成果 · 网页）"],"translations":{"zh-CN":{"title":"Anthropic 用 Claude 在 11 天内完成费马大定理首个机器验证的 Lean 形式化证明","summary":"Anthropic 发布首个完整经计算机验证的费马大定理证明，Claude 在 11 天内大体自主完成形式化，写出 1300 万行 Lean 代码并证明 30，300 个定理（最终使用其中 29，500 个），规模超过 Mathlib 5 倍以上。","category":"行业动态","source":"Anthropic","aggregationSource":"Anthropic：Research（发表成果 · 网页）","pageTitle":"Anthropic 用 Claude 在 11 天内完成费马大定理首个机器验证的 Lean 形式化证明 - Aioga AI资讯","description":"Anthropic 发布首个完整经计算机验证的费马大定理证明，Claude 在 11 天内大体自主完成形式化，写出 1300 万行 Lean 代码并证明 30，300 个定理（最终使用其中 29，500 个），规模超过 Mathlib 5 倍以上。","url":"https://www.aioga.com/news/cmtnapudv01zbrog16o6dxgoi/","articleBody":["我们分享费马大定理的首个完整的计算机检查证明。克洛德在11天内几乎自主地用精益编程语言编写了证明。下面，我们将描述形式化过程，并分享对这项工作对数学研究可能带来的影响的一些想法。大约在1637年，皮埃尔·德·费马在他著的《丢番图算术》边注记下了一个主张，这成为史上最著名的数学猜想之一：对于任意n>2，没有正整数a、b、c满足aⁿ + bⁿ = cⁿ。费马大定理：https：//www.youtube.com/watch？v=1BSFyEIY2BY（FLT），这一猜想证明极其困难。1995年安德鲁·怀尔斯爵士提出的第一个证明长达129页，经过数月的艰苦验证。","十年后，荷兰计算机科学家Jan Bergstra提出了“形式化”怀尔斯证明：将数学推理转化为计算机能自动检查的形式。从那时起，数学家们一直在开发编码如此复杂证明的方法，包括2024年由帝国理工学院的Kevin Buzzard发起的多年社区努力，利用精益证明Lean_助手完成了形式化：https：//lean-lang.org/use-cases/flt/（proof_assistant）。","最近，哥伦比亚大学人类学研究员彭天一，其团队致力于构建人工智能形式化工具，着手测试克劳德是否能取得FLT形式化的进展。结果超出了他的预期。在11天内，克劳德几乎自主地完成了FLT的首个端到端、计算机检查证明。在此过程中，他编写了1300万行精益理论，并证明了29500条中间定理。","我们将所得的证明分享给了 Kevin Buzzard，他说：","自动形式化像FLT这样复杂的证明，是迈向未来数学都能被轻松检验的重要一步。随着人工智能产生越来越多的证明，能够轻松形式化工作，可以减轻评估新结果（这一过程可能需要数年）。我们希望，信任构成数学的知识体系会变得更容易，而非更困难。","不同于最近由人工智能驱动的关于黎曼假设的工作（例如：https://www.anthropic.com/research/riemann-zeta），这些工作产生了新的数学内容，这里的新颖之处在于验证——像使用计算器检查数学计算一样检查数学证明。证明数学定理需要组装复杂的逻辑链，如果其中任何一个环节出错，之后的所有内容都可能是错误的。深入理解一个新的结果并对其正确性有信心，可能需要数月甚至数年的工作。","费马大定理是一个说明性的例子。费马在一本书的页边写下了定理的陈述，并附上一条引人注意的说明：","350 多年来，一代又一代的数学家都在寻找费马大定理的证明，无论是惊人的还是常规的。1908年，为了奖励任何能提出正确证明的人，宣布了10万德国金马克的奖金（相当于今天的100万到200万美元），仅在第一年就产生了621个不正确的尝试。","1993年6月，韦尔斯在为期三天的系列讲座中展示了他认为是第一份正确的费马大定理证明。在几位数学家进行的密集验证工作两个月后，一位审稿人向韦尔斯提出了一个问题，暴露了关键的漏洞。韦尔斯花了一年时间尝试修复，先是独自一人，然后与他的前学生理查德·泰勒合作。当他几乎要放弃这个项目时，他最终意识到自己早先放弃的一种方法可以修复证明。韦尔斯于1995年5月发表了费马大定理的第一份正确证明；该证明依赖于现代数学技术，这些技术远超费马在1637年所知。由于经过数百年的努力仍未找到初等证明，数学界现在认为费马自称的“惊人证明”实际上是不正确的：https://mathenchant.wordpress.com/2016/05/16/fermats-last-theorem-the-curious-incident-of-the-boasting-frenchman/。","检查证明正确性的一种方法是让计算机来做。像 Lean 这样的证明助手可以算法化地验证证明的逻辑，毫无疑问地展示其正确性。对于人类来说，困难的部分是改写证明以便 Lean 能理解。为人类读者编写的证明会跳过许多显而易见的步骤，而 Lean 需要看到每一步，无论多么微不足道。人类的证明也建立在数个世纪的已发表工作之上，而形式化证明则是从已经形式化的数学的一小部分开始。","对于费马大定理（FLT），形式化过程预计将耗费数年时间。仅仅是蓝图：https://imperialcollegelondon.github.io/FLT/blueprint.pdf 数学界用来描述项目初期阶段就有 86 页。","Claude 在 11 天内完成了证明，在此过程中产生了 30,300 个计算机可验证的定理（最终证明中使用了 29,500 个）。数十个 Claude 代理协作定义概念、证明中间定理，并使用这些定理去证明更难的命题。Claude 的证明有 1,300 万行 Lean 代码，其规模超过 Mathlib 的 5 倍，Mathlib 是该定理所依赖的主要社区数学证明库。3","Claude 的证明遵循 Darmon、Diamond 和 Taylor 的 Wiles 证明的简化版本：https://www.math.mcgill.ca/darmon/pub/Articles/Expository/05.DDT/paper.pdf。人类数学输入仅限于 Tianyi 的偶尔高级指令：“Jacobian 作为一个 scheme 看起来优先级很高”，“尽快完成 [Mazur 定理]”。你可以在这里找到 Claude 思考的摘录：https://www-cdn.anthropic.com/9e431dff043da6538d99d6c2d231b670aa3da263.pdf。","Claude 在意识到自己刚刚完成的成果时的思考摘录。","Claude 的最初尝试中有若干失败：尽管代理早期取得了一些成功，但他们很快失去了对项目状态的跟踪，停止了有效协作。他们失败的尝试贡献了最终证明中约 7% 的非模板化代码行。","当我们转向使用 Prove2Me：https://prove2me.vercel.app/ 时，这项工作得以成功，这是一种由 Tianyi Peng 及其哥伦比亚大学的合作团队设计的开放协作数学形式化平台。Prove2Me 通过以下方式提供了帮助：","通过 Prove2Me 和基于 Claude Code 的多智能体系统，一个智能体团队在不到两周的时间内完成了证明，消耗了大约六十亿个通用内部研究模型的输出令牌，该模型大致相当于 Claude Fable 5.1。最终的证明经过 Lean 检查；它仅使用 Lean 的三个标准公理，以及一个比较器：https://github.com/leanprover/comparator，确认定理的陈述与 Mathlib 自身对 FLT 的陈述一致。","我们能够如此快速地生成这一证明表明，现在有可能形式化大量数学，这既可能发现数学已知证明中的错误，也可以减轻审阅新工作的负担。在审查 Claude 的 Lean 证明后，Kevin Buzzard 告诉我们：","形式化也是人类对 AI 生成的数学结果建立信心的一个重要因素。随着 AI 和 AI 辅助数学家产生的（所谓）证明比以往更多，AI 辅助的形式化减轻了人类审阅者的一部分负担。我们预计，在为人类读者准备的任何写作中，同时生成形式化证明将变得普遍。虽然我们认为形式化证明不应取代人类可理解的阐述，但它可能是数学界跟上 AI 生成贡献的唯一可行方法。","编写 Lean 代码似乎也有助于 Claude 证明新颖结果。我们最近许多由 Claude 创作的结果都是在其证明的同时进行形式化的，Claude 似乎利用这些部分证明独立检查其假设，就像它编写数值模拟以确认自己方向正确一样。","形式化 FLT 是一个令牌密集型项目，但它也是迄今为止构建的最大 Lean 证明。Anthropic 的研究人员做了一个小实验，使用三个个人 Claude Max 计划来形式化 Hardy-Littlewood 圆法的应用。完全通过 Prove2Me 协作，智能体们在短短三天内共同完成了 Vinogradov 三素数定理的形式化：https://en.wikipedia.org/wiki/Vinogradov%27s_theorem。我们认为，有了合适的支架，通过消费者 AI 订阅进行重大结果的协作形式化是可实现的。","为此，Anthropic：https://www.anthropic.com/news/expanding-support-for-scientists 以及其他实验室：https://openai.com/index/chatgpt-for-academic-researchers/ 最近扩大了对外部研究人员的支持——包括从事纯数学和形式化研究的数学家——提供免费和折扣订阅以及研究积分。我们还提供专项资助：https://www.anthropic.com/news/ai-for-science-program，用于更大规模的科学项目，这可能包括形式化其他重大定理或改进 Lean 或 Mathlib。","随着 AI 快速改变数学研究的面貌，数学家们——在 Anthropic 及其他地方——正在思考这对他们的工作意味着什么：https://leidendeclaration.ai/。然而，形式化是我们对 AI 作用感到明确肯定的一个领域。随着形式化成为一种更普遍的工具，我们希望它能帮助维护数学知识的共同信任基础。","我们的形式化工作是费马大定理和形式数学发展的悠久历史中的一小部分。Andrew Wiles 与 Richard Taylor 的首次完整证明是三百多年数学工作的顶点，整合了 Gerhard Frey、Jean-Pierre Serre、Ken Ribet、Barry Mazur、Robert Langlands、Jerrold Tunnell、Yutaka Taniyama、Goro Shimura 以及 André Weil 等人的思想。Claude 的证明遵循 Henri Darmon、Fred Diamond 和 Richard Taylor 的阐述：https://www.math.mcgill.ca/darmon/pub/Articles/Expository/05.DDT/paper.pdf。","我们的证明借鉴了 Kevin Buzzard 领导的伦敦帝国学院 FLT 项目：https://github.com/ImperialCollegeLondon/FLT 以及 flt-regular 项目：https://github.com/leanprover-community/flt-regular 的部分成果。Lean 和 Mathlib 本身是各自的心血结晶，得到了数百名数学家的贡献，其中许多人与 Lean FRO：https://lean-lang.org/fro/ 合作。我们感谢 Kevin Buzzard 对证明进行审阅并提出意见。","完整证明以及书面的证明详解可在 GitHub 上获取：https://github.com/anthropics/fermats-last-theorem","我们让 Claude 自主训练模型，以提高它们在几个公共基准测试上对 10 类对齐失败的表现。对于所有 10 类，Claude 都找到了改进的方法，在不降低能力的情况下提升了目标基准的表现。","在本文中，我们分享两个结果，展示 Claude 如何帮助生命科学家加快他们的研究进程。","涉及 AI 辅助发现、实用工作流程以及各科学领域的实地笔记的特性内容。"]},"en":{"title":"Claude completed the first fully machine-verified proof of Fermat's Last Theorem in 11 days","summary":"Anthropic released the first fully machine-verified proof of Fermat's Last Theorem. Claude basically completed it autonomously in 11 days, writing 13 million lines of Lean code and proving 29,500 intermediate theorems.","category":"Industry","source":"Anthropic：Research（发表成果 · 网页）","aggregationSource":"Anthropic：Research（发表成果 · 网页）","pageTitle":"Claude completed the first fully machine-verified proof of Fermat's Last Theorem in 11 days - Aioga AI News","description":"Anthropic released the first fully machine-verified proof of Fermat's Last Theorem. Claude basically completed it autonomously in 11 days, writing 13 million lines of Lean code and...","url":"https://www.aioga.com/en/news/cmtnapudv01zbrog16o6dxgoi/","contentTranslated":true,"sourceHash":"3627cd978f914555","translatedAt":"2026-09-05T16:20:13.590Z"},"ja":{"title":"クロードはフェルマーの最終定理の初の完全な機械検証証明を11日で完成させる","summary":"Anthropicは、フェルマーの最終定理の初の完全な機械検証証明を発表。クロードは11日間でほぼ自律的に完成させ、1,300万行のLeanコードを書き、29,500の中間定理を証明した。","category":"業界動向","source":"Anthropic：Research（发表成果 · 网页）","aggregationSource":"Anthropic：Research（发表成果 · 网页）","pageTitle":"クロードはフェルマーの最終定理の初の完全な機械検証証明を11日で完成させる - Aioga AIニュース","description":"Anthropicは、フェルマーの最終定理の初の完全な機械検証証明を発表。クロードは11日間でほぼ自律的に完成させ、1,300万行のLeanコードを書き、29,500の中間定理を証明した。","url":"https://www.aioga.com/ja/news/cmtnapudv01zbrog16o6dxgoi/","contentTranslated":true,"sourceHash":"3627cd978f914555","translatedAt":"2026-09-05T16:20:14.187Z"},"ko":{"title":"Claude는 11일 만에 페르마의 마지막 정리의 첫 번째 완전한 기계 검증 증명을 완료했습니다.","summary":"Anthropic은 첫 번째 완전한 기계 검증 페르마의 마지막 정리 증명을 발표했습니다. Claude는 11일 만에 거의 자율적으로 1,300만 줄의 Lean 코드를 작성하고 29,500개의 중간 정리를 증명했습니다.","category":"업계 동향","source":"Anthropic：Research（发表成果 · 网页）","aggregationSource":"Anthropic：Research（发表成果 · 网页）","pageTitle":"Claude는 11일 만에 페르마의 마지막 정리의 첫 번째 완전한 기계 검증 증명을 완료했습니다. - Aioga AI 뉴스","description":"Anthropic은 첫 번째 완전한 기계 검증 페르마의 마지막 정리 증명을 발표했습니다. Claude는 11일 만에 거의 자율적으로 1,300만 줄의 Lean 코드를 작성하고 29,500개의 중간 정리를 증명했습니다.","url":"https://www.aioga.com/ko/news/cmtnapudv01zbrog16o6dxgoi/","contentTranslated":true,"sourceHash":"3627cd978f914555","translatedAt":"2026-09-05T16:20:16.959Z"},"es":{"title":"Claude completó en 11 días la primera verificación completa por máquina del gran teorema de Fermat","summary":"Anthropic publicó la primera demostración del gran teorema de Fermat completamente verificada por máquina, que Claude completó casi de manera autónoma en 11 días, escribiendo 13 millones de líneas de código Lean y demostrando 29,500 teoremas intermedios.","category":"Industria","source":"Anthropic：Research（发表成果 · 网页）","aggregationSource":"Anthropic：Research（发表成果 · 网页）","pageTitle":"Claude completó en 11 días la primera verificación completa por máquina del gran teorema de Fermat - Aioga Noticias de IA","description":"Anthropic publicó la primera demostración del gran teorema de Fermat completamente verificada por máquina, que Claude completó casi de manera autónoma en 11 días, escribiendo 13 mi...","url":"https://www.aioga.com/es/news/cmtnapudv01zbrog16o6dxgoi/","contentTranslated":true,"sourceHash":"3627cd978f914555","translatedAt":"2026-09-05T16:20:16.213Z"},"fr":{"title":"Claude a terminé en 11 jours la première preuve entièrement vérifiée par machine du dernier théorème de Fermat","summary":"Anthropic a publié la première preuve entièrement vérifiable par machine du dernier théorème de Fermat, que Claude a réalisée presque de manière autonome en 11 jours, en écrivant 13 millions de lignes de code Lean et en prouvant 29 500 théorèmes intermédiaires.","category":"Industrie","source":"Anthropic：Research（发表成果 · 网页）","aggregationSource":"Anthropic：Research（发表成果 · 网页）","pageTitle":"Claude a terminé en 11 jours la première preuve entièrement vérifiée par machine du dernier théorème de Fermat - Aioga Actualités IA","description":"Anthropic a publié la première preuve entièrement vérifiable par machine du dernier théorème de Fermat, que Claude a réalisée presque de manière autonome en 11 jours, en écrivant 1...","url":"https://www.aioga.com/fr/news/cmtnapudv01zbrog16o6dxgoi/","contentTranslated":true,"sourceHash":"3627cd978f914555","translatedAt":"2026-09-05T16:20:19.059Z"},"de":{"title":"Claude schloss den ersten vollständigen maschinell verifizierten Beweis des Fermatschen Satzes in 11 Tagen ab","summary":"Anthropic veröffentlichte den ersten vollständig maschinell verifizierten Beweis des Fermatschen Satzes, wobei Claude diesen in 11 Tagen weitgehend eigenständig erstellte, 13 Millionen Zeilen Lean-Code schrieb und 29.500 Zwischensätze bewies.","category":"行业动态","source":"Anthropic：Research（发表成果 · 网页）","aggregationSource":"Anthropic：Research（发表成果 · 网页）","pageTitle":"Claude schloss den ersten vollständigen maschinell verifizierten Beweis des Fermatschen Satzes in 11 Tagen ab - Aioga KI-News","description":"Anthropic veröffentlichte den ersten vollständig maschinell verifizierten Beweis des Fermatschen Satzes, wobei Claude diesen in 11 Tagen weitgehend eigenständig erstellte, 13 Milli...","url":"https://www.aioga.com/de/news/cmtnapudv01zbrog16o6dxgoi/","contentTranslated":true,"sourceHash":"3627cd978f914555","translatedAt":"2026-09-05T16:20:18.533Z"},"pt-BR":{"title":"Claude completou a primeira prova de verificação mecânica do Último Teorema de Fermat em 11 dias","summary":"A Anthropic lançou a primeira prova do Último Teorema de Fermat verificada mecanicamente, que Claude completou quase de forma autônoma em 11 dias, escrevendo 13 milhões de linhas de código Lean e provando 29.500 teoremas intermediários.","category":"行业动态","source":"Anthropic：Research（发表成果 · 网页）","aggregationSource":"Anthropic：Research（发表成果 · 网页）","pageTitle":"Claude completou a primeira prova de verificação mecânica do Último Teorema de Fermat em 11 dias - Aioga Notícias de IA","description":"A Anthropic lançou a primeira prova do Último Teorema de Fermat verificada mecanicamente, que Claude completou quase de forma autônoma em 11 dias, escrevendo 13 milhões de linhas d...","url":"https://www.aioga.com/pt-BR/news/cmtnapudv01zbrog16o6dxgoi/","contentTranslated":true,"sourceHash":"3627cd978f914555","translatedAt":"2026-09-05T16:20:20.555Z"},"ru":{"title":"Клод завершил первую полноценную машинную проверку доказательства Великой теоремы Ферма за 11 дней","summary":"Anthropic опубликовала первое полноценное машинное доказательство Великой теоремы Ферма, Клод почти самостоятельно завершил его за 11 дней, написав 13 миллионов строк кода на Lean и доказав 29 500 промежуточных теорем.","category":"行业动态","source":"Anthropic：Research（发表成果 · 网页）","aggregationSource":"Anthropic：Research（发表成果 · 网页）","pageTitle":"Клод завершил первую полноценную машинную проверку доказательства Великой теоремы Ферма за 11 дней - Aioga Новости ИИ","description":"Anthropic опубликовала первое полноценное машинное доказательство Великой теоремы Ферма, Клод почти самостоятельно завершил его за 11 дней, написав 13 миллионов строк кода на Lean...","url":"https://www.aioga.com/ru/news/cmtnapudv01zbrog16o6dxgoi/","contentTranslated":true,"sourceHash":"3627cd978f914555","translatedAt":"2026-09-05T16:20:21.414Z"},"ar":{"title":"كلود أنجز التحقق الكامل الأولي لآلة من نظرية فيرما الكبرى في 11 يومًا","summary":"أنتروبيك نشرت أول إثبات كامل ومتحقق منه آليًا لنظرية فيرما الكبرى، حيث أكمل كلود المهمة بشكل شبه مستقل خلال 11 يومًا، وكتب 13 مليون سطر من كود Lean وأثبت 29,500 نظرية وسيطة.","category":"行业动态","source":"Anthropic：Research（发表成果 · 网页）","aggregationSource":"Anthropic：Research（发表成果 · 网页）","pageTitle":"كلود أنجز التحقق الكامل الأولي لآلة من نظرية فيرما الكبرى في 11 يومًا - Aioga أخبار الذكاء الاصطناعي","description":"أنتروبيك نشرت أول إثبات كامل ومتحقق منه آليًا لنظرية فيرما الكبرى، حيث أكمل كلود المهمة بشكل شبه مستقل خلال 11 يومًا، وكتب 13 مليون سطر من كود Lean وأثبت 29,500 نظرية وسيطة.","url":"https://www.aioga.com/ar/news/cmtnapudv01zbrog16o6dxgoi/","contentTranslated":true,"sourceHash":"3627cd978f914555","translatedAt":"2026-09-05T16:20:24.035Z"},"hi":{"title":"Claude ने 11 दिनों में फ़र्मा के अंतिम सिद्धांत का पहला पूरी तरह से मशीन-पुष्ट प्रमाण पूरा किया","summary":"Anthropic ने फ़र्मा के अंतिम सिद्धांत का पहला पूरी तरह से मशीन-पुष्ट प्रमाण जारी किया, जिसे Claude ने लगभग स्वायत्त रूप से 11 दिनों में पूरा किया, 13 मिलियन लाइनों का Lean कोड लिखा और 29,500 मध्यवर्ती प्रमेयों को प्रमाणित किया।","category":"行业动态","source":"Anthropic：Research（发表成果 · 网页）","aggregationSource":"Anthropic：Research（发表成果 · 网页）","pageTitle":"Claude ने 11 दिनों में फ़र्मा के अंतिम सिद्धांत का पहला पूरी तरह से मशीन-पुष्ट प्रमाण पूरा किया - Aioga AI समाचार","description":"Anthropic ने फ़र्मा के अंतिम सिद्धांत का पहला पूरी तरह से मशीन-पुष्ट प्रमाण जारी किया, जिसे Claude ने लगभग स्वायत्त रूप से 11 दिनों में पूरा किया, 13 मिलियन लाइनों का Lean कोड लिखा...","url":"https://www.aioga.com/hi/news/cmtnapudv01zbrog16o6dxgoi/","contentTranslated":true,"sourceHash":"3627cd978f914555","translatedAt":"2026-09-05T16:20:23.940Z"},"it":{"title":"Claude ha completato la prima verifica completa della dimostrazione del grande teorema di Fermat in 11 giorni","summary":"Anthropic ha rilasciato la prima dimostrazione del grande teorema di Fermat verificata completamente da macchina, Claude l'ha completata quasi autonomamente in 11 giorni, scrivendo 13 milioni di righe di codice Lean e dimostrando 29.500 teoremi intermedi.","category":"行业动态","source":"Anthropic：Research（发表成果 · 网页）","aggregationSource":"Anthropic：Research（发表成果 · 网页）","pageTitle":"Claude ha completato la prima verifica completa della dimostrazione del grande teorema di Fermat in 11 giorni - Aioga Notizie IA","description":"Anthropic ha rilasciato la prima dimostrazione del grande teorema di Fermat verificata completamente da macchina, Claude l'ha completata quasi autonomamente in 11 giorni, scrivendo...","url":"https://www.aioga.com/it/news/cmtnapudv01zbrog16o6dxgoi/","contentTranslated":true,"sourceHash":"3627cd978f914555","translatedAt":"2026-09-05T16:20:25.798Z"},"nl":{"title":"Claude voltooide de eerste volledige machine-verifieerbare bewijs van de Grote Stelling van Fermat in 11 dagen","summary":"Anthropic publiceerde het eerste volledig machine-verifieerbare bewijs van de Grote Stelling van Fermat, dat Claude bijna volledig zelfstandig in 11 dagen voltooide, met 13 miljoen lijnen Lean-code en het bewijs van 29.500 tussenliggende stellingen.","category":"行业动态","source":"Anthropic：Research（发表成果 · 网页）","aggregationSource":"Anthropic：Research（发表成果 · 网页）","pageTitle":"Claude voltooide de eerste volledige machine-verifieerbare bewijs van de Grote Stelling van Fermat in 11 dagen - Aioga AI-nieuws","description":"Anthropic publiceerde het eerste volledig machine-verifieerbare bewijs van de Grote Stelling van Fermat, dat Claude bijna volledig zelfstandig in 11 dagen voltooide, met 13 miljoen...","url":"https://www.aioga.com/nl/news/cmtnapudv01zbrog16o6dxgoi/","contentTranslated":true,"sourceHash":"3627cd978f914555","translatedAt":"2026-09-05T16:20:25.357Z"},"tr":{"title":"Claude, Fermat'nın Büyük Teoremi için ilk tam makine doğrulamalı kanıtı 11 günde tamamladı","summary":"Anthropic, ilk tam makine doğrulamalı Fermat'nın Büyük Teoremi kanıtını yayımladı; Claude bunu 11 gün içinde neredeyse bağımsız şekilde tamamladı, 13 milyon satır Lean kodu yazdı ve 29.500 ara teoremi kanıtladı.","category":"行业动态","source":"Anthropic：Research（发表成果 · 网页）","aggregationSource":"Anthropic：Research（发表成果 · 网页）","pageTitle":"Claude, Fermat'nın Büyük Teoremi için ilk tam makine doğrulamalı kanıtı 11 günde tamamladı - Aioga AI Haberleri","description":"Anthropic, ilk tam makine doğrulamalı Fermat'nın Büyük Teoremi kanıtını yayımladı; Claude bunu 11 gün içinde neredeyse bağımsız şekilde tamamladı, 13 milyon satır Lean kodu yazdı v...","url":"https://www.aioga.com/tr/news/cmtnapudv01zbrog16o6dxgoi/","contentTranslated":true,"sourceHash":"3627cd978f914555","translatedAt":"2026-09-05T16:20:27.954Z"},"vi":{"title":"Claude đã hoàn thành bằng chứng kiểm chứng máy tính đầu tiên về định lý lớn Fermat trong 11 ngày","summary":"Anthropic đã công bố bằng chứng kiểm chứng máy tính đầu tiên về định lý lớn Fermat, và Claude hầu như tự động hoàn thành trong 11 ngày, viết 13 triệu dòng mã Lean và chứng minh 29.500 định lý trung gian.","category":"行业动态","source":"Anthropic：Research（发表成果 · 网页）","aggregationSource":"Anthropic：Research（发表成果 · 网页）","pageTitle":"Claude đã hoàn thành bằng chứng kiểm chứng máy tính đầu tiên về định lý lớn Fermat trong 11 ngày - Tin tức AI Aioga","description":"Anthropic đã công bố bằng chứng kiểm chứng máy tính đầu tiên về định lý lớn Fermat, và Claude hầu như tự động hoàn thành trong 11 ngày, viết 13 triệu dòng mã Lean và chứng minh 29....","url":"https://www.aioga.com/vi/news/cmtnapudv01zbrog16o6dxgoi/","contentTranslated":true,"sourceHash":"3627cd978f914555","translatedAt":"2026-09-05T16:20:27.707Z"},"id":{"title":"Claude menyelesaikan bukti verifikasi mesin penuh pertama Teorema Terakhir Fermat dalam 11 hari","summary":"Anthropic merilis bukti Teorema Terakhir Fermat yang difverifikasi sepenuhnya oleh mesin untuk pertama kalinya, Claude pada dasarnya menyelesaikannya secara mandiri dalam 11 hari, menulis 13 juta baris kode Lean dan membuktikan 29.500 teorema menengah.","category":"行业动态","source":"Anthropic：Research（发表成果 · 网页）","aggregationSource":"Anthropic：Research（发表成果 · 网页）","pageTitle":"Claude menyelesaikan bukti verifikasi mesin penuh pertama Teorema Terakhir Fermat dalam 11 hari - Berita AI Aioga","description":"Anthropic merilis bukti Teorema Terakhir Fermat yang difverifikasi sepenuhnya oleh mesin untuk pertama kalinya, Claude pada dasarnya menyelesaikannya secara mandiri dalam 11 hari,...","url":"https://www.aioga.com/id/news/cmtnapudv01zbrog16o6dxgoi/","contentTranslated":true,"sourceHash":"3627cd978f914555","translatedAt":"2026-09-05T16:20:29.619Z"},"th":{"title":"Claude ใช้เวลา 11 วันในการทำการพิสูจน์ทฤษฎีบทใหญ่ของแฟร์มาต์ด้วยเครื่องครั้งแรกให้สมบูรณ์","summary":"Anthropic เผยแพร่การพิสูจน์ทฤษฎีบทใหญ่ของแฟร์มาต์ด้วยเครื่องครั้งแรกที่สมบูรณ์ Claude ทำงานแทบจะอิสระภายใน 11 วัน เขียนโค้ด Lean จำนวน 13 ล้านบรรทัดและพิสูจน์ทฤษฎีย่อยกลางจำนวน 29,500 เรื่อง","category":"行业动态","source":"Anthropic：Research（发表成果 · 网页）","aggregationSource":"Anthropic：Research（发表成果 · 网页）","pageTitle":"Claude ใช้เวลา 11 วันในการทำการพิสูจน์ทฤษฎีบทใหญ่ของแฟร์มาต์ด้วยเครื่องครั้งแรกให้สมบูรณ์ - ข่าว AI Aioga","description":"Anthropic เผยแพร่การพิสูจน์ทฤษฎีบทใหญ่ของแฟร์มาต์ด้วยเครื่องครั้งแรกที่สมบูรณ์ Claude ทำงานแทบจะอิสระภายใน 11 วัน เขียนโค้ด Lean จำนวน 13 ล้านบรรทัดและพิสูจน์ทฤษฎีย่อยกลางจำนวน 29,...","url":"https://www.aioga.com/th/news/cmtnapudv01zbrog16o6dxgoi/","contentTranslated":true,"sourceHash":"3627cd978f914555","translatedAt":"2026-09-05T16:20:30.704Z"},"pl":{"title":"Claude ukończył pierwsze pełne komputerowe weryfikowane dowodzenie Wielkiego Twierdzenia Fermata w ciągu 11 dni","summary":"Anthropic opublikował pierwsze pełne komputerowe weryfikowane dowodzenie Wielkiego Twierdzenia Fermata, które Claude w zasadzie samodzielnie ukończył w ciągu 11 dni, pisząc 13 milionów linii kodu w Lean i dowodząc 29 500 twierdzeń pośrednich.","category":"行业动态","source":"Anthropic：Research（发表成果 · 网页）","aggregationSource":"Anthropic：Research（发表成果 · 网页）","pageTitle":"Claude ukończył pierwsze pełne komputerowe weryfikowane dowodzenie Wielkiego Twierdzenia Fermata w ciągu 11 dni - Aioga Wiadomości AI","description":"Anthropic opublikował pierwsze pełne komputerowe weryfikowane dowodzenie Wielkiego Twierdzenia Fermata, które Claude w zasadzie samodzielnie ukończył w ciągu 11 dni, pisząc 13 mili...","url":"https://www.aioga.com/pl/news/cmtnapudv01zbrog16o6dxgoi/","contentTranslated":true,"sourceHash":"3627cd978f914555","translatedAt":"2026-09-05T16:20:32.952Z"}},"evidenceTier":"verified-news","reviewStatus":"editorial-selected","indexable":true,"editorialCover":""}}