OpenAI Says AI System Solved Navier-Stokes Millennium Problem

Multi-agent system generated and checked the proposed proof

OpenAI said the discovery phase came from an internal model significantly more capable than GPT-6 Astra, described as its most advanced publicly available model. Roughly 10,000 agents worked together for 88 hours on the problem, which has remained unresolved for about 90 years. The agents exchanged 2.7 million messages and generated roughly 130 billion tokens before GPT-6 Astra spent another 17 hours formalizing and checking the resulting proof.

Sebastien Bubeck, a researcher at OpenAI, separately said about 10,000 agents were working on the problem at one point. OpenAI head of research Mark Chen said the compute bill exceeded the $1 million value of the Clay prize. OpenAI has said it will not seek the prize money.

The Clay Mathematics Institute has not recognized the proof. Its requirements call for a proposed solution to be published through a qualifying outlet, remain publicly available for two years and receive broad acceptance from mathematicians before the institute considers awarding the prize. The result therefore remains a proposed solution subject to prolonged mathematical scrutiny despite OpenAI also producing a machine-checkable formalization in the Lean proof language.

OpenAI has said the significance of the underlying research system could extend beyond this particular problem. The same multi-agent approach could eventually be directed at difficult research in materials science, energy, aerospace, medicine and other scientific fields, according to the material describing the project.

Buckmaster and Alpöge question how OpenAI reached the approach

NYU mathematician Tristan Buckmaster and Anthropic researcher Levent Alpöge had spent roughly one year pursuing a closely related route involving a smooth external force and had used AI tools, including OpenAI’s Codex, extensively in their work. Buckmaster said almost nobody else he knew was following the same approach and questioned how OpenAI arrived at it within days of learning that he and Alpöge had made progress.

Buckmaster said he was initially shown a prompt during discussions with OpenAI and told the internal research effort had begun with no human input beyond the problem statement. According to Buckmaster, that account changed during subsequent conversations, when OpenAI acknowledged that the first prompt had been sent only in the preceding days after information about his and Alpöge’s work had reached the company.

Buckmaster said he had initially been told there was “very little human input” in the result. He later said calls with OpenAI showed that an entire team had been involved, that easier problems had been tackled first and that the prompt shown to him had itself been generated by prompting Codex.

Buckmaster has not accused OpenAI of definitively taking the unpublished research. He wrote in a public statement, “I do not know whether our data was used.” OpenAI says neither its researchers nor its agents saw Buckmaster and Alpöge’s prompts, drafts or user data before the work became public and that no specific user data was accessed to generate its proof.

OpenAI nevertheless included a qualification in its response: “While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models.” Alpöge reacted by posting, “i mean props to them for straight coming clean,” after flagging that language.

OpenAI also says its proof differs substantially from the work produced by Buckmaster and Alpöge. That distinction leaves the dispute focused not only on whether specific unpublished material was accessed, but also on whether de-identified product usage could have influenced models used in later research.

Disagreement also emerged over credit and release coordination

Buckmaster’s statement said OpenAI had floated “proposals” that included removing Alpöge’s name from an announcement attributing the Navier-Stokes solution to OpenAI’s internal model. Bubeck disputed that characterization.

Bubeck said a screenshot under discussion showed him reaching out to Alpöge “to coordinate our releases” and wrote on September 8, 2026: “I never ever asked for Levent to be removed from authorship of his own work.” Sam Altman also publicly backed OpenAI’s team.

Buckmaster credited the underlying research program to mathematicians Diego Córdoba and Luis Martínez-Zoroa rather than to an AI system. He called the episode a “Deep Blue-Kasparov” turning point for mathematics.

Buckmaster has not filed any lawsuit. OpenAI continues to maintain that no specific user data was accessed and that its proof is substantially different from the other researchers’ work, while its acknowledgment that de-identified usage data could not be completely ruled out has left the provenance issue unresolved.

The broader question raised by the dispute concerns research conducted through commercial AI systems whose developers are also building frontier research tools. The issue centers on how unpublished work entered into those products may contribute to model improvement, how attribution should work and how any downstream influence could be demonstrated.