On September 8, 2026, OpenAI revealed that an internal AI model had produced a solution to the Navier–Stokes existence and smoothness problem, one of the seven Millennium Prize Problems carrying a $1 million reward. This announcement follows rumors that other researchers had also made progress on the problem.
The news has been met with dispute from Tristan Buckmaster, a mathematics professor at New York University, and Levent Alpöge, a mathematician employed by Anthropic. Buckmaster and Alpöge had been collaborating on related mathematical challenges for almost a year, leveraging AI tools such as Claude and Codex, primarily GPT-5.6 Sol. They reported a breakthrough on August 15, 2026.
According to Buckmaster, after learning that OpenAI was working on a similar problem, he inquired about when OpenAI’s AI model had first been prompted regarding the Navier–Stokes problem. OpenAI initially did not provide a direct answer but later indicated the first prompt was sent only days after they became aware of Buckmaster and Alpöge’s work. Buckmaster also questioned whether OpenAI’s model had been trained on or accessed their private Codex sessions, which contained their drafts. OpenAI denied accessing user data but did not clarify if their training data included de-identified information derived from those sessions.
OpenAI stated their effort began on September 1, 2026, after hearing rumors of recent breakthroughs on Millennium Prize problems. Their AI agents resolved the Navier–Stokes problem by September 5, using extensive computational resources—sending 2.7 million messages and generating approximately 130 billion output tokens. The full verification process took an additional 17 hours using GPT-6 Astra.
OpenAI offered to coordinate a joint announcement with Buckmaster and Alpöge to acknowledge their priority but declined to include Alpöge as a co-author due to competitive concerns related to his employer, Anthropic. OpenAI emphasized that their proofs differ significantly from those of Buckmaster and Alpöge, particularly in the Euler case.
This episode highlights emerging challenges in AI-assisted mathematical research, especially regarding data privacy and intellectual property. It raises questions about how AI models trained on user data might inadvertently influence subsequent problem-solving efforts by others. The situation also reflects broader concerns about competitive dynamics in AI research, where rapid developments can lead to disputes over priority and credit.
The controversy underscores the need for clearer policies on data usage and collaboration in AI-driven scientific discovery, as well as the potential impact of AI on accelerating solutions to longstanding open problems.