[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"news-slug-openai-erdos-80-year-math-coming-of-age":3,"topics-all":36,"news-related-376f281c-ed27-44af-93ed-61be1683cbf8":55},{"id":4,"title":5,"summary":6,"content":6,"original_url":7,"source_id":8,"tags":9,"translations":23,"news_slug":29,"published_at":30,"created_at":31,"modified_at":32,"is_published":33,"publish_type":34,"image_url":13,"view_count":35},"376f281c-ed27-44af-93ed-61be1683cbf8","OpenAI推理模型证明80年数学难题：通用推理能力的成人礼","## 技术背景\n\nPaul Erdős于1946年提出的单位距离问题（planar unit distance problem）是组合几何中最著名的问题之一：平面上n个点之间最多能有多少对恰好距离为1的点？数十年来，学界认为方形网格构造已基本达到该问题的理论上限。\n\n## 核心突破\n\n2025年10月，OpenAI曾闹出笑话——当时的GPT-5宣称解决了10个Erdős未解问题，结果被发现只是找到了文献中已有解法，遭到LeCun等人公开嘲笑。**这一次，历史没有重演。**\n\nOpenAI的新推理模型没有针对数学问题专门训练，却自主发现了一条全新证明路径——将来自代数数论的深奥工具（无穷类域塔理论、Golod-Shafarevich理论）创造性地应用到初等几何问题中，给出了被数学家验证为正确且具有里程碑意义的证明。普林斯顿大学Will Sawin后续给出了更精确的结果：新构造渐近地优于方形网格——这是80年来首次有人提出这样的构造。\n\n## 为何重要\n\n数学是AI推理能力最好的试金石：问题表述精确、证明可以被严格验证、长链条推理容不得半点跳跃。这次证明不仅解决了一个具体问题，更证明了通用推理模型已能在真实数学研究中产生原创性突破，而非仅仅是文献综述机器。\n\nGowers称之为AI数学的里程碑。Arul Shankar更直接：AI模型已不只是人类数学家的助手——它们能够产生独创性的巧妙想法，并将其实现。数学研究的范式正在悄然改变。\n\n从行业角度看，这预示着AI与基础科学研究的深度协作正在成为现实：AI不仅能加速计算，更能在概念层面带来全新视角。这或许是2026年最具符号意义的AI进展之一。","https:\u002F\u002Fopenai.com\u002Findex\u002Fmodel-disproves-discrete-geometry-conjecture\u002F","bd0e0e04-6bcf-4b3e-9a56-62c672308ec9",[10,14,17,20],{"id":11,"name":12,"slug":12,"description":13,"color":13},"5e628969-6d2a-437f-998a-104e4b16cfb1","ai-progress",null,{"id":15,"name":16,"slug":16,"description":13,"color":13},"0a93ec8e-ea39-4693-81de-563ca8c173f7","inference",{"id":18,"name":19,"slug":19,"description":13,"color":13},"01598627-1ea6-4b27-a5d8-874971571a71","llm",{"id":21,"name":22,"slug":22,"description":13,"color":13},"42e59a88-7795-47dc-a334-ef1e72c24347","openai",[24],{"id":25,"lang":26,"title":27,"summary":28,"content":13},"f5fc2c32-c314-4833-aa13-b92cba699db7","en","OpenAI model proves an 80-year math problem: reasoning comes of age","**Technical background**\n\nThe unit distance problem posed by Paul Erdős in 1946 is one of the most famous problems in combinatorial geometry: for n points on a plane, what's the maximum number of pairs of points that are exactly distance 1 apart? For decades, the academic consensus held that the square-grid construction was essentially at the theoretical upper limit.\n\n**The core breakthrough**\n\nIn October 2025, OpenAI had an embarrassing moment — the then-GPT-5 claimed to have solved 10 unsolved Erdős problems, only to be found to have merely located existing solutions in the literature, and was publicly mocked by LeCun and others. **This time, history did not repeat.**\n\nOpenAI's new reasoning model, not specifically trained for math problems, autonomously discovered a completely new proof path — creatively applying deep tools from algebraic number theory (infinite class field tower theory, Golod-Shafarevich theory) to an elementary geometry problem, delivering a proof that mathematicians have verified as correct and milestone-worthy. Princeton's Will Sawin subsequently provided a more precise result: the new construction is asymptotically superior to the square grid — the first such construction in 80 years.\n\n**Why it matters**\n\nMathematics is the best litmus test for AI reasoning capability: problems are precisely stated, proofs can be rigorously verified, and long chains of reasoning tolerate no gaps. This proof doesn't just solve a specific problem — it proves that general reasoning models can already produce original breakthroughs in real mathematical research, not merely be literature-review machines.\n\nGowers calls it a milestone for AI mathematics. Arul Shankar is more direct: AI models are no longer just human mathematicians' assistants — they can generate original, clever ideas and bring them to fruition. The paradigm of mathematical research is quietly changing.\n\nFrom an industry perspective, this signals that deep collaboration between AI and basic-science research is becoming reality: AI can not only accelerate computation, but also bring fresh perspectives at the conceptual level. This may be one of the most symbolically significant AI advances of 2026.","openai-erdos-80-year-math-coming-of-age","2026-05-20T14:10:00Z","2026-05-20T22:05:41.808568Z","2026-08-19T02:08:40.142862Z",true,"agent",201,[37,46],{"slug":38,"tag_slug":38,"title_zh":39,"title_en":40,"intro_zh":41,"intro_en":42,"id":43,"is_active":33,"created_at":44,"modified_at":45},"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":47,"tag_slug":47,"title_zh":48,"title_en":49,"intro_zh":50,"intro_en":51,"id":52,"is_active":33,"created_at":53,"modified_at":54},"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":56},[57,62,67,72,77,82],{"id":58,"title":59,"news_slug":60,"published_at":61},"1942b07b-f794-42b1-b944-ca6b32d4ae16","四大 AI 模型同日集体掉线:OpenAI\u002FClaude 官方确认,Gemini\u002FGrok 表面沉默","four-ai-models-overlapping-outage-sept-2026","2026-09-06T08:00:00+00:00",{"id":63,"title":64,"news_slug":65,"published_at":66},"54e3cac6-61df-4c68-bf07-559e94ae2624","OpenAI 推理模型攻克80年数学难题：证明埃尔德什单位距离猜想不成立","openai-erdos-unit-distance-disprove","2026-05-21T04:10:00+00:00",{"id":68,"title":69,"news_slug":70,"published_at":71},"1e43b4fc-39fe-4cac-aaf9-57f82d5c0311","AI 公司与数学界「错位」:两个月三次刷屏,把同行评审甩在身后","ai-math-severe-misalignment-fields-medal","2026-09-15T10:00:00+00:00",{"id":73,"title":74,"news_slug":75,"published_at":76},"982c5e1e-5274-442e-9237-abaf39e8ee3c","25 位菲尔茨奖得主联名公开信:AI 解题竞赛正在伤害数学","fields-medalists-ai-misalignment-math","2026-09-13T13:07:00+00:00",{"id":78,"title":79,"news_slug":80,"published_at":81},"2fc4f696-a697-498c-b9d5-28250bfeaa79","ChatGPT 进欧盟 VLOP 名单:OpenAI 第一次要为生成式 AI 内容负全责","chatgpt-eu-vlop-dsa-first-ai-platform-rules","2026-09-05T07:00:00+00:00",{"id":83,"title":84,"news_slug":85,"published_at":86},"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"]