Mathematician Alleges OpenAI Pursued Navier–Stokes Breakthrough After Learning of His Work

Mathematician Tristan Buckmaster alleges that OpenAI pursued a potential breakthrough on the Navier–Stokes problem shortly after learning about research he had been conducting with Anthropic researcher Levent Alpöge.

The dispute began on September 3, when Buckmaster said he heard that information about his and Alpöge’s work had reached OpenAI. 

Buckmaster then contacted OpenAI to explain that he and Alpöge were already working on the problem and had planned to publish their results. 

Three days later, on September 6, he spoke twice with OpenAI technical staff member Sébastien Bubeck and another company representative about the two groups’ work.

According to Buckmaster, Bubeck told him the internal model had produced the Navier–Stokes proof. When Alpöge asked what exactly the model had solved, Buckmaster said OpenAI described it as a result showing that the equations could develop a blow-up in three dimensions when an external force is applied under specific conditions.

That description concerned Buckmaster because it followed the same broad approach he and Alpöge had been pursuing. “When I heard ‘forced,’ it was a bright red flag,” he wrote.

Buckmaster said he was initially told that OpenAI’s model had been given the Navier–Stokes problem with “very little human input”. 

But, he said, further discussion revealed that the effort involved “an entire team” and was “one of a number of things that was tried”. 

According to Buckmaster, the team had first used the model on easier mathematical problems, “including Euler”, before turning to the Navier–Stokes problem. 

He also said he was told that “an insane amount of compute” had been used.

The timing of that effort became a key point for Buckmaster. 

He said he repeatedly asked when OpenAI had first prompted the model to work on the problem, but did not initially receive a direct answer. He said it was eventually established that the first prompt had been sent “in the past few days” — after information about his and Alpöge’s work had reached OpenAI.

That led Buckmaster to raise a separate question about the private Codex sessions he and Alpöge had used throughout their project. “I asked whether the model had been trained on, or had access to, our sessions in Codex, into which we had been putting all our drafts for the whole of this project,” he wrote. 

Buckmaster said he was told that the model did not look up user data, but said he did not receive an answer to the separate question of whether material from those sessions could have been incorporated into training.

Buckmaster has stressed that this does not establish that OpenAI used his work. He said he has not seen the company’s alleged proof and does not know what the model did, how it produced its result, or whether his data was used. “I am not accusing anyone of anything,” he wrote.

The disagreement then extended to how the results would be published. Buckmaster said OpenAI proposed two options: he and Alpöge could publish their Euler result, followed by OpenAI publishing its Navier–Stokes result the next day; or Buckmaster could write a paper presenting the Navier–Stokes result himself, while acknowledging that an internal OpenAI model had produced it.

Buckmaster also alleged that Bubeck twice argued that Alpöge should not be an author because he works for Anthropic. 

Buckmaster said he rejected the proposal. Bubeck has disputed Buckmaster’s broader account, saying on X that “false and inflammatory allegations” about him were circulating. He said he had handled the discussion according to academic norms and would give a fuller response.

Buckmaster is an NYU Courant Institute mathematician known for work on fluid dynamics and Navier–Stokes, and Alpöge is a mathematician and Anthropic researcher who collaborated with Buckmaster on the forced blow-up work.

The Navier–Stokes problem describes how fluids such as air and water move and is one of the seven Millennium Prize Problems. 

A proof resolving whether smooth solutions can develop singularities would settle a fundamental question in mathematical physics and carries a $1 million prize from the Clay Mathematics Institute.