美国克雷数学研究所（Clay Mathematics Institute）于千禧年设立的七大千禧年大奖难题各悬赏100万美元，此前仅有一道被数学家攻克。2026年9月8日，人工智能研究机构OpenAI宣布其AI智能体集群成功解决了困扰数学界逾一个世纪的“纳维-斯托克斯方程存在性与光滑性问题”。该方程组是描述三维固定密度流体流动的核心物理工具，广泛应用于航空气动力学、管道输运与天体物理学；千禧年难题聚焦于该方程是否会在有限时间内因速度等物理量无限激增而产生“奇点”，从而导致经典方程彻底失效。
据OpenAI披露，其研发团队于8月28日训练了具备代码执行与跨网络协作功能的新模型，并于9月1日部署智能体集群攻关千禧年难题。在投入运算50小时后，由约100个智能体组成的子群解答了该领域的一项前置关键问题，科研团队随即引导约1万个智能体全面聚焦纳维-斯托克斯问题。最终在历时88小时、产生270万条交互信息并耗费超过650万美元算力成本后，AI集群通过构造一个速度无限制激增的旋转流体漩涡，成功证明了流体运动中奇点的客观存在。
然而，这一重磅突破随即引发了关于科研伦理与优先权的激烈纷争。纽约大学数学家特里斯坦·巴克马斯特（Tristan Buckmaster）与Anthropic研究员莱文特·阿尔珀格（Levent Alpöge）此前已在AI辅助下接近完整证明，在与OpenAI合作谈判破裂后抢先于网络公开了未完成手稿。巴克马斯特质疑其团队在借助OpenAI工具研究时的成果可能被吸纳进了后者的训练数据，OpenAI亦承认无法排除这一数据污染可能。尽管OpenAI表态不会申请百万美元奖金，但这一事件对科学发现的成果归属界定与数学学科的未来演进提出了深层次挑战。
On September 8th OpenAI announced that a swarm of its artificial-intelligence agents had resolved the Navier-Stokes existence and smoothness problem, marking only the second solution to the seven Millennium Prize problems established by the Clay Mathematics Institute. Governing fluid dynamics across aerospace engineering, internal pipeline flows, and stellar astrophysics, the century-old Navier-Stokes equations describe three-dimensional fluid motion. The fundamental Millennium conjecture interrogated whether these equations inevitably break down in finite time through the emergence of a mathematical singularity—a point where physical variables such as velocity escalate toward infinity, invalidating classical physical descriptions.
OpenAI detailed an unprecedented deployment of autonomous computational power to conquer the mathematical challenge. Initiating model training on August 28th, researchers unleashed collaborative AI agents equipped to synthesize internet research, execute verification scripts, and communicate autonomously. After 50 hours of exploratory processing, a sub-group solved an adjacent foundational lemma, prompting scientists to channel roughly 10,000 agents solely toward the Navier-Stokes equations. Over an 88-hour computational burst that generated 2.7m internal agent messages and consumed more than $6.5m in hardware infrastructure, the agent ensemble derived an analytical solution: a spiraling fluid vortex demonstrating runaway velocity growth that culminates in an undeniable singularity.
However, the purported breakthrough has triggered intense academic discord regarding data integrity and intellectual attribution. Prior to the public announcement, New York University mathematician Tristan Buckmaster and Anthropic researcher Levent Alpöge had neared their own AI-supported proof, prompting Buckmaster to post pre-print findings online after collaborative discussions with OpenAI collapsed. Buckmaster alleged that proprietary research conducted using OpenAI tools may have inadvertently leaked into the company's training corpora, a scenario OpenAI conceded it could not definitively dismiss. While OpenAI confirmed it will forgo the $1m Clay prize, the episode exposes critical unresolved dilemmas concerning machine-generated discoveries, provenance, and the evolving nature of human scientific exploration.
Source: OpenAI's apparent maths breakthrough raises profound questions
Subtitle: It has stirred controversy about how the discipline should work
Dateline: Sep 10th 2026