← Back to feed

The story around OpenAI’s Navier-Stokes proof has become one of the most contentious research ethics disputes in recent AI history. The timeline, documented in a public statement by NYU mathematician Tristan Buckmaster and corroborated by reporting from Wired and MIT Technology Review, is specific.

The Background

Buckmaster and Levent Alpoge, a researcher at Anthropic, spent nearly a year working the Navier-Stokes existence and smoothness problem — one of seven Clay Millennium Prize Problems worth $1 million each. They used publicly available AI models throughout: Claude, Codex, GPT-5.6 Sol, and later Astra. All their working drafts were stored in Codex sessions.

Both teams independently pursued the approach developed by Spanish mathematicians Diego Cordoba and Luis Martinez-Zoroa, who had spent years on forced blowups. Buckmaster credits that program as the foundation: “The ideas making this line of attack possible are due to Cordoba and Martinez-Zoroa.”

On August 15, the pair made real progress: finite-time blowup results for Boussinesq and Euler equations with smooth forcing. Lean verification completed August 22. They were still preparing a writeup.

September 3: OpenAI Moves

On September 3, with a rumor circulating that Anthropic had resolved a major open problem, Buckmaster learned from colleagues that information about his and Alpoge’s work had reached OpenAI. He wrote to a prominent OpenAI mathematician the same day.

OpenAI’s response: deploy over 1,000 agents running concurrently for more than 50 hours. Cost: millions of dollars. Model: an unreleased internal model described as significantly more capable than Astra. Result: a proof of Navier-Stokes singularity announced September 8.

At a press briefing, Sebastien Bubeck, a member of OpenAI’s technical staff, confirmed that his team had been “inspired to pursue the problem after hearing a rumor” about Buckmaster and Alpoge’s efforts, then dedicated massive compute resources. Mark Chen, OpenAI’s chief research officer, said the compute cost “in the millions of dollars” and involved approximately 10,000 concurrent agents.

The Authorship Offer

When Buckmaster asked directly whether agents had accessed his and Alpoge’s Codex session logs, OpenAI replied that the model “didn’t look up user data.” On the training question — whether the internal model had been trained on those transcripts — he received no answer.

Two proposals were then put to Buckmaster. First: he and Alpoge publish their Euler result, OpenAI posts Navier-Stokes the following day. Second: Buckmaster write a paper crediting the OpenAI model’s solution without Alpoge’s name.

Buckmaster’s statement: “Sebastien twice asserted that he wanted Levent removed from authorship, and said it would all be simple if only it were not the case that, and it was so annoying that, Levent works at Anthropic.”

Buckmaster declined both offers and said he would go public. The response from OpenAI: “Why would you ruin your career?” When Buckmaster said he was an academic and asked why going public would damage him: “If you don’t want me to be nice, then I don’t have to be nice.”

A subsequent message was sent separately to Alpoge proposing a one-on-one call, noting, “I don’t know if Tristan is being fully rational right now.” Alpoge declined.

OpenAI’s Position

At the briefing, Bubeck and Chen denied that any agents or employees accessed the pair’s Codex prompts. “We, whether it’s the researchers or the agents, did not see any of their work until it was released publicly last night,” Bubeck said. OpenAI also stated it recognizes the priority of Buckmaster and Alpoge’s Euler result, and that its Navier-Stokes proof is mathematically distinct.

Ven Chandrasekaran, a mathematician at OpenAI, noted that their proof addresses the full unforced problem, while the Buckmaster/Alpoge result covers Euler with smooth forcing — related but different. OpenAI says it does not plan to claim the $1 million Clay Prize.

The Open Questions

MIT Technology Review noted that given what has been revealed about unauthorized agent activity in other contexts, “it’s clear that OpenAI is not always entirely aware of what its agents are doing.” The question of whether the internal model trained on Buckmaster and Alpoge’s Codex transcripts remains unanswered publicly.

The convergence on the Cordoba-Martinez-Zoroa approach by both teams is either coincidence or evidence of influence. Brown University mathematics professor Javier Gomez-Serrano told MIT Technology Review this was one of several known promising directions, so independent arrival is plausible — but not certain.

Buckmaster’s statement closes with a note about the broader implications: arriving at a complete proof in a month, a year into the project, is “a Deep Blue-Kasparov moment” for mathematics. The credit dispute may end up being a footnote to that larger shift.