Key Points

  • OpenAI announced that its AI model has generated a Lean-verified proof indicating that the Navier-Stokes fluid equations can "blow up," utilizing 10,000 AI agents over 88 hours.
  • Shortly before this, NYU mathematician Tristan Buckmaster accused OpenAI's Sébastien Bubeck of being aware of his unpublished proof and pressuring him for credit prior to the announcement.
  • OpenAI, Bubeck, and CEO Sam Altman have denied these allegations; Bubeck shared messages he claims show he offered Buckmaster's team the chance to publish first.

On Tuesday, OpenAI declared that its internal AI model had solved a significant question in mathematical research, but the announcement triggered backlash after allegations from NYU mathematician Tristan Buckmaster surfaced, claiming unethical conduct by the company.

OpenAI's assertion centers on proving that the Navier-Stokes equations, which describe fluid dynamics, can experience a "blow up"—a scenario where the equations predict infinite speed, an impossibility in reality.

This problem is one of the seven Millennium Prize Problems, each carrying a $1 million reward from the Clay Mathematics Institute.

According to OpenAI, the solution was derived over 88 hours with approximately 10,000 AI agents working in coordination, validated by Lean, a software that checks mathematical proofs step by step.

We’re sharing a solution to the Navier-Stokes Millennium Prize Problem, one of the deepest problems at the frontier of mathematics.

The proof was produced by a group of agents, using an OpenAI next-generation model significantly more capable than GPT-6 Astra.

The problem… pic.twitter.com/8zol3BPTL4

— OpenAI (@OpenAI) September 8, 2026

However, it appears that they may not have been the first to arrive at this conclusion.

Just hours ahead of OpenAI's announcement, Buckmaster released a four-page statement revealing that he and Levent Alpöge, a mathematician at rival firm Anthropic, had dedicated nearly a year to using AI models to pursue proofs of fluid blow-up, achieving a solution by August 22.

Buckmaster claims that on September 3, amidst speculation that Anthropic had solved a major issue, he informed an OpenAI mathematician about their project, emphasizing that it was personal and not affiliated with either organization.

Three days later, during a phone call, Bubeck informed him that OpenAI's internal model had already developed a 100-page proof for the forced Navier-Stokes problem, the same specific approach Buckmaster asserts was largely ignored by others.

Buckmaster alleges that Bubeck proposed two choices: either OpenAI would publish the day after Buckmaster's team or Buckmaster would write his paper alone, excluding Alpöge due to his affiliation with a competing laboratory. When Buckmaster opted for public disclosure, Bubeck reportedly responded, "Why would you ruin your career?"

Buckmaster ultimately published his findings, with credit given to Alpöge, but neither received acknowledgment from OpenAI—aside from a quote tweet stating that it could not “rule out that de-identified data derived from their usage of our products helped improve our models.”

OpenAI and Bubeck Respond

Bubeck, along with OpenAI and Altman, refutes Buckmaster’s version of events. In a subsequent post, Bubeck shared messages suggesting a coordinated release with Alpöge and stated he acted with integrity.

“I hope it’s clear from the message that we came in with the best possible intentions,” he wrote. “I never ever asked for Levent to be removed from authorship of his own work.”

OpenAI CEO Sam Altman defended Bubeck, asserting he "acted with integrity and generosity throughout," and mentioned that the company proposed allowing Buckmaster's team to publish first once they realized that the other team had only solved Euler's equations, not the complete Navier-Stokes problem.

I spent much of the weekend talking with the team who did this work. Seb--and everyone else--acted with integrity and generosity throughout.

Initially we believed the other team had also solved the problem. We wanted to collaborate and do a joint release.

When we learned that… https://t.co/XESh5oFHHE

— Sam Altman (@sama) September 8, 2026

In a separate statement, OpenAI clarified that it had not seen Buckmaster and Alpöge's work prior to publication and did not access any specific user data; however, the company did not completely dismiss the possibility either.

Fields Medalist Terence Tao praised the mathematical work of Buckmaster and Alpöge as a "remarkable achievement." This incident marks the second notable AI-math development from the same two labs within a week, following Anthropic's claim that Claude produced a computer-verified proof of Fermat's Last Theorem.

Buckmaster and Alpöge's most advanced findings, which are closest to addressing the $1 million problem, remain unpublished pending final verification with Lean. No external reviewers have assessed OpenAI's 100-page proof as of yet.