OpenAI Announces Three Major AI-Driven Scientific Breakthroughs Across Math, Complexity Theory and Physics

OpenAI 于 10 月 26 日宣布其 AI 模型在数学、计算机科学与物理学三个领域产出三项重大科学发现，规模罕见，横跨调和分析、复杂性理论与量子场论，其中两项与千禧年大奖难题直接相关。公司称已提供 Lean 形式化验证并组织独立学术审查，学界在震惊之余高度关注验证进展。

已确认

• 数学：OpenAI 发布前印本（官方 repo openai/math，已有 16k stars），称 AI 发明新的数学技术「局部平滑用于欧氏波动方程」，证明了 1991 年提出的局部光滑猜想（全维度），并借此同时解决所有维度下的 Kakeya 猜想与 Stein 限制猜想，还解决了 35 年未解的波聚焦问题。此前该方向仅有 2019 年 Guth-Wang-Zhan 的二维结果与 2025 年的三维进展。
• 计算机科学：模型声称证伪指数时间假设（ETH），该假设断言 3-SAT 等问题不存在亚指数时间算法，是复杂性理论与大量下界证明的基石。据 m17 转述，理论计算机学者 Ryan Williams 宣布 OpenAI 内部模型产出了对 ETH 的反驳；Andrew Curran 亦在 X 上贴出论文链接宣称 ETH 不成立。若 3SAT 存在亚指数算法，由于 3SAT 是 NP 完全问题，影响将极其深远。
• 物理学：据 m4 转述 OpenAI 官方博客「Building scientific understanding with academic communities」，模型于 2026 年 9 月 9 日产出 Yang-Mills 存在性（千禧年大奖难题）证明并完成 Lean 形式化；m7、m16 亦提及量子色动力学（QCD）存在性与标准模型相关结果。
• 前OpenAI 总裁 Greg Brockman、Polymarket 等均公开发布了这一消息；Polymarket 上「OpenAI 年底前宣布又一道千禧年大奖难题获解」的市场概率为 54%。
• 学界正在组织独立审查；多条帖子显示 Andrew Curran、Ryan Williams 等学者已介入讨论。

尚未确认

• 各项证明尚未（在帖子材料范围内）通过完整同行评审，均为「宣称」性质，有待独立审查结论。
• 帖子间存在信息分歧：多数帖子归因于 OpenAI，m7 则称消息来自 danintheory（harmonic 相关团队）的 Harmonic AI；m13 称共有四项成果而非三项。以 OpenAI 官方发布为准的版本为三项。
• m8 的作者 esrtweet 观察到圈内开始讨论「ETH 为假是否暗示 P=NP」，其本人仍倾向 P≠NP，但表示过去 4 小时内把握明显下降——这属于猜测而非结论。

为什么重要

• 若证明成立，ETH 被证伪将动摇数百篇论文赖以成立的复杂性理论基础与密码学下界证明。密码学家 Matthew Green 惊叹这一结果比预期来得早得多，原以为要到感恩节前后才会出现如此「怪异」的突破，并调侃两周前对模型能力局限颇有定见的人没人预测到这一进展。
• Yang-Mills 存在性是克雷千禧年大奖难题，Kakeya 猜想与 Stein 限制猜想是调和分析核心开放问题，AI 同时在三个领域逼近或解决顶级难题，被视为 AI 从工具转向「科学发现主体」的标志性事件，正如 Brockman 所言，或标志着 AI 开始切实帮助人类加深对宇宙的理解。

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