OpenAI claims Navier-Stokes solve amid academic controversy

OpenAI claims to have solved Navier-Stokes Millennium Prize problem

OpenAI announced on Tuesday, September 9, 2026, that it had solved one of the Millennium Prize problems, the Navier-Stokes equations that describe fluid motion. The company said its unreleased model found a solution in just 88 hours by deploying a swarm of about ten thousand internal AI agents. It called the result a milestone and noted that the problem has resisted human mathematicians for nearly ninety years, even though a one-million-dollar prize from the Clay Mathematics Institute awaits a verified proof.

The timing of the announcement raised eyebrows because just one day earlier, on September 8, a New York University mathematics professor named Tristan Buckmaster had posted work on a related problem together with Levent Alpöge, a researcher at Anthropic, OpenAI’s rival. Buckmaster said he reached out to OpenAI after learning the company had become aware of their progress, asking when OpenAI began its effort and what data had trained its model. According to Buckmaster, the conversation quickly turned hostile. An OpenAI researcher reportedly asked why he would risk his career by going public, and when he pressed for clarification, the reply was that niceness was optional if he did not want it. OpenAI then urged him to publish the findings while crediting its internal model and removing Alpöge as a co-author.

Allegations that OpenAI accessed private Codex sessions of NYU professor

Buckmaster also said he inquired whether OpenAI had accessed his private sessions on Codex, a tool he used while working on the problem. He described the company’s responses as increasingly evasive and even hostile. In later statements, OpenAI denied using any specific user data to achieve the result. It said its researchers and agents did not see any of the external team’s work before it was released publicly, and that no personal data was accessed for the solve. At the same time, the company acknowledged that it could not completely rule out the possibility that de-identified information derived from users’ interactions with its products might have indirectly influenced model improvements, while emphasizing that the two proofs differ substantially.

OpenAI researcher Sébastien Bubeck told a press briefing, as reported by Science, that the effort began after the company spotted rumors on Twitter that other groups were making headway on Millennium Prize questions. The team reacted by asking why they should not try to solve one themselves given the strength of their model. Only later did they realize the rumors concerned Alpöge and Buckmaster. Bubeck has since disputed parts of Buckmaster’s account, denying that he ever asked the NYU professor to drop Alpöge from the author list.

The company characterized the undertaking as hurried and extremely costly, saying it spent millions of dollars on the push. Yet OpenAI said it has no intention of claiming the Clay Institute’s bounty, which remains unawarded, and that its sole aim was to showcase the progress of its AI systems. It added that it had not publicly worked on Navier-Stokes before September, or if it had, it had not disclosed any such effort.

Even leaving aside the most serious allegations, aspects of OpenAI’s behavior that the firm itself has acknowledged have unsettled mathematicians. Abhishek Saha, a professor at Queen Mary University of London, said the company had engaged in practices that most mathematicians would consider unacceptable. The rush to beat other researchers to a result contrasts with the discipline’s usual norms, where openness and deep specialization make scooping difficult, though not impossible. The episode has sparked worries that such tactics could chill collaborative work in mathematics, a field that has long prized sharing ideas over racing to priority.

For those who build or use AI, the episode highlights both the power

Frequently asked questions

What did OpenAI announce about the Navier-Stokes equations on September 9, 2026?

OpenAI announced that it had solved the Navier-Stokes Millennium Prize problem, claiming its unreleased model found a solution in 88 hours using a swarm of about ten thousand internal AI agents, calling the result a milestone.

How did OpenAI describe the resources and timeline for its Navier-Stokes effort?

OpenAI said the effort began after spotting Twitter rumors, took 88 hours, involved roughly ten thousand internal AI agents, and cost millions of dollars, though it described the undertaking as hurried and extremely costly.

What allegations did Tristan Buckmaster raise regarding OpenAI’s conduct and data use?

Buckmaster said OpenAI reacted hostilely after he shared his work, asked why he would risk his career, urged him to publish while crediting OpenAI’s model and removing Alpöge as co-author, and questioned whether OpenAI accessed his private Codex sessions, receiving evasive replies.

What is OpenAI’s position on claiming the Clay Mathematics Institute’s $1 million prize for the Navier-Stokes solution?

OpenAI said it has no intention of claiming the Clay Institute’s bounty, which remains unawarded, and that its sole aim was to showcase the progress of its AI systems rather than to win the prize.

Source: The Verge