OpenAI于9月5日通过内部AI Agent解决了纳维-斯托克斯存在性与光滑性问题，这是七个千禧年大奖问题之一，每项悬赏100万美元1。该Agent在约88小时内完成求解，验证过程耗时17小时，共发送490万条消息并使用约3000亿个输出Token1。按公开API价格估算，该项目的计算成本约为1500万美元1。
然而这一成就引发了学术优先权纠纷。纽约大学数学教授Tristan Buckmaster与Anthropic员工Levent Alpöge早在8月15日已取得相似突破，他们使用Claude和Codex工作近一年1。Buckmaster指出OpenAI在获悉他们工作信息后才启动项目，他表示："我问他们第一个提示何时发送。OpenAI长时间没有直接回答。最终同意是在关于我们工作的信息到达他们之后的过去几天发送的"1。他还询问新模型训练中是否使用过他们的Codex会话数据，但称"我没有得到答案"1。
OpenAI首席执行官Sam Altman随后发表声明澄清争议。Altman表示OpenAI团队成员"以诚信和慷慨的态度始终如一地行动"2，并称OpenAI初期误认为对方团队也已解决纳维-斯托克斯方程问题，因此主动提议让对方先发表2。他指出对方团队仅解决了欧拉方程而非纳维-斯托克斯方程2。OpenAI在声明中强调："我们的证明差异显著，甚至在欧拉情况下证明的确切结果也不同（有强制与无强制）"1。
OpenAI announced that its AI Agent successfully solved the Navier-Stokes existence and smoothness problem, one of seven Millennium Prize Problems, on September 5, 2026 1. The breakthrough came approximately 88 hours after the company initiated the project on September 1 following rumors about the problem's potential solution 1. The verification process required 17 hours of computation, with the Agent sending 4.9 million messages and consuming approximately 300 billion output tokens across all research, including 2.7 million messages and 1.3 billion tokens specifically dedicated to the Navier-Stokes problem 1. Based on public API pricing, this computational effort would cost approximately $15 million 1.
The achievement has become mired in controversy over academic priority and data usage. NYU mathematics professor Tristan Buckmaster and Anthropic employee Levent Alpöge claimed they achieved a breakthrough on August 15, after working for nearly a year using Claude and Codex 1. Buckmaster stated: "I asked them when the first prompt was sent. OpenAI took a long time to give a direct answer. They finally agreed it was sent in the past few days after information about our work reached them" 1. He further raised concerns about whether OpenAI's new model incorporated their Codex session data during training, noting "I didn't get an answer" 1. However, the two teams' accomplishments differ significantly: Buckmaster and Alpöge solved only the Euler equation, not the full Navier-Stokes equation 2.
OpenAI CEO Sam Altman addressed the dispute in a statement, claiming that OpenAI initially believed both teams had solved the Navier-Stokes problem and proposed a joint publication 2. Upon discovering the other team had only solved the Euler equation variant, OpenAI offered to let them publish first and suggested Buckmaster author a rewritten version of OpenAI's proof 2. Altman emphasized that OpenAI team members "have consistently acted with integrity and generosity" and stated "I never asked Levent to remove himself from the authorship of his own work" 2. OpenAI's proof differs substantially from the competing work, with different results even in the Euler case regarding boundary conditions 1. The Millennium Prize Problems have offered $1 million per problem since May 24, 2000 1.
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