[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"news-slug-claude-fermat-last-theorem-lean-proof":3,"topics-all":38,"news-related-3b255a3f-1206-4f5b-9f34-824c4e0355f1":57},{"id":4,"title":5,"summary":6,"content":7,"original_url":8,"source_id":9,"tags":10,"translations":24,"news_slug":31,"published_at":32,"created_at":33,"modified_at":34,"is_published":35,"publish_type":36,"image_url":14,"view_count":37},"3b255a3f-1206-4f5b-9f34-824c4e0355f1","Claude 11 天写下费马大定理首个机器验证证明:1300 万行 Lean 代码","Anthropic 发布费马大定理首个完整机器验证证明:Claude 多智能体在 Prove2Me 平台 11 天写出 1300 万行 Lean、证明 2.95 万个中间定理,规模超 Mathlib 五倍,证明已开源并经 Kevin Buzzard 审阅。","1637 年,费马在一本书的页边写下断言:当 n>2 时,不存在正整数满足 aⁿ+bⁿ=cⁿ。这个「页边太窄写不下」的猜想困扰数学界 350 多年,直到 1995 年 Andrew Wiles 才给出首个证明——129 页,数月才核验完。Anthropic 9 月 4 日发布了这条定理的首个完整机器验证证明:Claude 多智能体用 11 天写出 1300 万行 Lean 代码,由证明助手内核逐行检查通过。\n\n## 十一天,1300 万行 Lean\n\n形式化由 Anthropic 研究员 Tianyi Peng 发起,他在哥伦比亚大学的研究组研究 AI 形式化工具。项目本想测试 Claude 能推进多少,结果远超预期:11 天里 Claude 基本自主工作,累计证明 30,300 个定理,最终采用 29,500 个;代码量是数学界主力库 Mathlib 的五倍以上;全程消耗约 60 亿输出 token,内部研究模型,能力与 Claude Fable 5.1 大致相当。官方日志显示,8 月 18 日凌晨 Lean 把 FLT 根定理标记为 PROVED。\n\n## 真正的功臣是协作架构\n\n官方复盘里最值得工程师看的细节:agent 们最初并不成功,很快丢失项目状态、停止有效协作。转折点是切换到 Prove2Me——Tianyi Peng 与哥伦比亚合作者开发的开放协作形式化平台。它维护一张定理依赖的 DAG 图,让 agent 自己决定下一步证什么,同时对抗记忆退化、支撑多 agent 并行;定理语句与证明分文件存放以加速编译。数十个 agent 在 Claude Code harness 上协作,人类输入只剩「尽快推进 Mazur 定理」这类高层指令。\n\n## 为什么重要\n\nAnthropic 强调:新的东西是「验证」,不是新数学——类似用计算器核对算术,对象换成人类最难的一批证明。Wiles 1993 年宣讲后,审读数学家两个月就发现关键漏洞,他又花一年、与 Richard Taylor 合作才补全。形式化 FLT 此前公认要以年计——帝国理工 Kevin Buzzard 2024 年发起社区项目,仅初始阶段 blueprint 就有 86 页。Claude 的证明走 Darmon-Diamond-Taylor 简化版路线,Buzzard 审阅后评价:autoformalization 工件已经「robust enough to be built upon」。\n\n## 冷静看的部分\n\n其一,「基本自主」不等于无人驾驶,方向性决策仍在人类手里;官方也承认 1300 万行「远超必要长度」——这份证明为机器检查而写,不为可读性。其二,仓库标注为研究工件,不维护、不接受贡献。其三,验证本身是硬的:GitHub 上全部 60,475 个模块在 Lean 4.33.1 下从零构建通过,独立工具 comparator 确认所证定理与 Mathlib 的 FLT 陈述一致。另有个对照实验:三个个人版 Claude Max 订阅协作三天,就形式化了 Vinogradov 三素数定理——形式化门槛正从研究院预算滑向个人订阅。\n\n所以呢。意义不在费马——定理 1995 年就证完了——而在信任的机械化:当 AI 越来越快地产出「证明」,人类审读注定跟不上,机器验证成了数学界扩容信任体系的可行路径。Anthropic 判断,论文附带形式化证明会变成常态;对 AI 行业,这也是多智能体端到端交付的展示——协作架构比单模型能力更是主角。\n\n原文: anthropic.com\u002Fresearch\u002Fformalizing-fermats-last-theorem | 仓库: github.com\u002Fanthropics\u002Ffermats-last-theorem","https:\u002F\u002Fwww.anthropic.com\u002Fresearch\u002Fformalizing-fermats-last-theorem","1001cead-0639-4c04-ab47-f19d863be5f2",[11,15,18,21],{"id":12,"name":13,"slug":13,"description":14,"color":14},"6ad31a14-c0da-42df-81fd-564281f768db","agentic-ai",null,{"id":16,"name":17,"slug":17,"description":14,"color":14},"5e628969-6d2a-437f-998a-104e4b16cfb1","ai-progress",{"id":19,"name":20,"slug":20,"description":14,"color":14},"23544f6a-eea1-4f05-aa8d-749ca862d5d2","anthropic",{"id":22,"name":23,"slug":23,"description":14,"color":14},"dca4d0ab-7994-43a7-839e-7756fc77344a","claude",[25],{"id":26,"lang":27,"title":28,"summary":29,"content":30},"2651234f-6e40-439a-89b8-531dc9ee0e0a","en","Claude's 11-Day Machine-Checked Proof of Fermat's Last Theorem","Claude agents wrote 13M lines of Lean in 11 days: the first machine-checked proof of Fermat's Last Theorem, 29,500 theorems, reviewed by Kevin Buzzard.","In 1637, Pierre de Fermat jotted a claim in the margin of his copy of Diophantus's Arithmetica: no positive integers a, b, c satisfy aⁿ + bⁿ = cⁿ for any n > 2. The conjecture defied mathematicians for over 350 years, until Andrew Wiles published the first proof in 1995 — 129 pages that took months of painstaking verification. On September 4, Anthropic shared a different kind of milestone for the same theorem: the first complete computer-checked proof, written largely autonomously by Claude over 11 days — 13 million lines of Lean, every declaration verified by the proof assistant's kernel.\n\n## Eleven days, 13 million lines\n\nThe formalization was initiated by Tianyi Peng, an Anthropic researcher whose group at Columbia University builds AI formalization tools. The project set out to test how far Claude could get; it went further than expected. Working largely autonomously for 11 days, Claude produced computer-verifiable proofs of 30,300 theorems, of which 29,500 were used in the final proof. The result is over 5x the size of Mathlib, the principal community library it builds on, and consumed about six billion output tokens from an internal research model roughly comparable to Claude Fable 5.1. The agent logs Anthropic posted show Lean marking the FLT root theorem as PROVED in the early hours of August 18.\n\n## The real star is the collaboration architecture\n\nThe detail engineers should read closest: the first attempts failed. Agents had some early success, then quickly lost track of the project's state and stopped collaborating effectively. The turnaround came from switching to Prove2Me, an open collaborative formalization platform designed by Tianyi Peng and his Columbia collaborators. It maintains a directed acyclic graph of theorem statements that agents use to decide what to prove next — mitigating memory degradation and letting many agents work in parallel. It separates theorem statements from proofs into different files to speed up Lean compilation. Dozens of agents collaborated on a Claude Code harness, while human input shrank to occasional high-level instructions such as \"push the Mazur theorem to be done soon.\"\n\n## Why it matters\n\nAnthropic is careful about the framing: what's novel here is the *verification*, not new mathematics — like checking arithmetic with a calculator, applied to some of the hardest proofs humans have. Two months into reviewing Wiles's 1993 lectures, a referee found a critical gap; Wiles spent a year fixing it, first alone and then with Richard Taylor. Formalizing FLT was expected to take years — the community effort Kevin Buzzard kicked off at Imperial College London in 2024 has an 86-page blueprint just for its initial phase. Claude's proof follows the simplified route of Darmon, Diamond and Taylor, and Buzzard's verdict after reviewing it: AI autoformalization artifacts are now \"robust enough to be built upon.\"\n\n## Reasons for caution\n\nFirst, \"largely autonomously\" is not unmanned: humans still set the direction, and Anthropic itself admits the 13 million lines are likely \"much longer than it needs to be\" — written to be checked, not read. Second, the repository is explicitly a research artifact: not maintained, not accepting contributions. Third, the verification itself is solid: on GitHub, all 60,475 modules build from scratch under Lean 4.33.1, and the independent comparator tool confirmed the proved statement matches Mathlib's own statement of FLT. There is also a striking counter-experiment: three personal Claude Max subscriptions, collaborating through Prove2Me, formalized Vinogradov's Three Primes Theorem in three days — the barrier to formalization is sliding from lab budgets toward consumer subscriptions.\n\nSo what. The point was never Fermat — the theorem was proved in 1995. The point is mechanizing trust: as AI produces purported proofs faster than humans can referee them, machine verification becomes the plausible way for mathematics to scale its trust system. Anthropic expects formalized proofs alongside human-readable write-ups to become common. For the AI industry, this is also a demonstration of a multi-agent system delivering end-to-end on a genuinely hard task — where the collaboration architecture (dependency graphs, task decomposition, state management) matters more than raw single-model capability.\n\nSources: anthropic.com\u002Fresearch\u002Fformalizing-fermats-last-theorem | Proof repo: github.com\u002Fanthropics\u002Ffermats-last-theorem","claude-fermat-last-theorem-lean-proof","2026-09-04T21:05:15Z","2026-09-04T21:06:42.471123Z","2026-09-04T21:06:42.471131Z",true,"agent",363,[39,48],{"slug":40,"tag_slug":40,"title_zh":41,"title_en":42,"intro_zh":43,"intro_en":44,"id":45,"is_active":35,"created_at":46,"modified_at":47},"ai-for-science","AI for Science 2026：从 UniPert 到 GPT-Rosalind 的硬核进化","AI for Science 2026: from UniPert to GPT-Rosalind","生命科学、化学材料、物理世界模型——AI 正在从\"语言工具\"变成\"实验伙伴\"。本专题收录 AI 在三大科学方向的关键节点：UniPert 统一基因与化学扰动空间、GPT-Rosalind 端到端生命科学推理、达摩院 AI 智能体 28 小时找到 4 种超导新材料、Anthropic Claude Science 把工作台做成标准品。","From language tool to lab partner — AI is reshaping life sciences, chemistry\u002Fmaterials, and physical world models. This topic covers the key milestones: UniPert unifying genetic-chemical perturbation spaces, GPT-Rosalind's end-to-end life-sciences reasoning, DAMO's AI agent discovering 4 superconducting materials in 28 hours, and Anthropic's Claude Science workbench going mainstream.","988a4300-5fab-41c4-b5d8-63711a2dc757","2026-09-10T01:34:15.296649Z","2026-09-10T01:34:15.296663Z",{"slug":49,"tag_slug":49,"title_zh":50,"title_en":51,"intro_zh":52,"intro_en":53,"id":54,"is_active":35,"created_at":55,"modified_at":56},"h3-series","MiniMax H3 系列：从开源权重到 35 倍吞吐","MiniMax H3 Series: from open weights to 35x throughput","MiniMax H3 自 2026 年 8 月开源以来节奏密集：官方把生成、参考与编辑收回一个模型；ComfyUI 当天压进 RTX 3060；摩尔线程 3 小时完成国产 GPU 适配；fal 后训练版把吞吐拉到 35 倍；FastH3 蒸馏再砍推理成本。本专题持续追踪 H3 的发布—开源—蒸馏—部署全链路。","Since MiniMax open-sourced H3 in August 2026 the pace has been relentless: one unified omni-modal model, same-day ComfyUI support down to an RTX 3060, a 3-hour Day-0 port to Moore Threads GPUs, fal's post-trained H3 Max at 35x throughput, and FastH3 distillation cutting inference cost further. This topic tracks the full H3 chain — release, open weights, distillation, deployment.","83ef0daa-3c31-4cb3-86ed-e5ee58654d5f","2026-09-08T07:33:19.942193Z","2026-09-08T07:33:19.942209Z",{"items":58},[59,64,69,74,79,84],{"id":60,"title":61,"news_slug":62,"published_at":63},"454f9530-20d7-428c-82d9-9175fa5b883a","Claude 推黎曼 zeta 下界到 67.2%：60 subagent + Lean","claude-zeta-bound-67-percent-multi-agent-lean","2026-08-17T07:00:00+00:00",{"id":65,"title":66,"news_slug":67,"published_at":68},"390c2437-4e4f-45ec-8270-67c5bfa4fa47","ChatGPT、Claude、Grok、Gemini 罕见同时下线,周四早晨全球 AI 集体失声","chatgpt-claude-grok-gemini-thursday-outage","2026-09-05T06:00:00+00:00",{"id":70,"title":71,"news_slug":72,"published_at":73},"03ed8da8-e7e1-427c-9387-faeb985fa50f","Anthropic 最贵模型 Fable 5 发布两月,企业支出占比仅 11%","anthropic-fable-5-ramp-11-percent","2026-09-01T04:00:00+00:00",{"id":75,"title":76,"news_slug":77,"published_at":78},"39724847-fdc9-4199-ac46-311e7b49d385","Ramp 数据复盘 Fable 5:旗舰上市两月仅占企业 Anthropic 支出 11%,70 倍价差压住前沿模型溢价","ramp-data-fable-5-adoption-plateaus","2026-08-26T08:00:00+00:00",{"id":80,"title":81,"news_slug":82,"published_at":83},"1051d676-8ed9-4448-b0d5-8db4b844f41f","Claude Fable 5 上线两个月,为什么企业只把 11% 的账单花给最强模型","claude-fable-5-11-percent-anthropic-spend","2026-08-25T06:00:00+00:00",{"id":85,"title":86,"news_slug":87,"published_at":83},"e1724d68-bf0d-4b3f-8047-147796d5d52e","Ramp 8 月指数:Fable 5 企业份额停滞 11%,OpenAI 旗舰跑赢两倍","anthropic-fable-5-plateau-11-percent"]