Dispute over math breakthrough: Who got to Navier-Stokes first?

The Navier-Stokes problem concerns how fluids and air move, and whether the underlying mathematics always yields "smooth" solutions. It is one of seven Millennium Problems from the Clay Mathematics Institute, with a $1 million prize for solving it. Now a dispute has erupted over who got there first with the help of AI.

Two announcements on the same day

On September 8, 2026, NYU professor Tristan Buckmaster and Anthropic mathematician Levent Alpöge published three proofs with a preliminary result on Navier-Stokes. They used both Claude and OpenAI's Codex. According to Buckmaster, they had spent almost a year chasing proofs with AI models and had a solution ready on August 22. Their most advanced result has not been released and is awaiting final verification in Lean, a program that checks mathematical proofs.

The same day, OpenAI announced that an internal, unreleased model using roughly 10,000 coordinated AI agents had produced a proof of about 100 pages in roughly 88 hours. According to Decrypt, it was verified with Lean.

TechCrunch reports that OpenAI's week-long effort, which also covered other unsolved problems, consumed about 300 billion output tokens, equivalent to an estimated $22.5 million in computing power at current prices. OpenAI began on September 1 after rumors that another team was close to a solution. The company confirms this.

Buckmaster's allegations

On September 3, Buckmaster told an OpenAI mathematician about his project. According to him, OpenAI's Sébastien Bubeck said in a call on September 6 that an internal model had already produced a proof. Buckmaster claims that Bubeck asked him to remove Alpöge's name as part of a compromise and offered poor publication options.

According to Buckmaster, Bubeck said: "Why would you ruin your career?" and later: "If you don't want me to be nice, then I don't have to be nice."

OpenAI denies the claims

OpenAI, Bubeck and Sam Altman reject Buckmaster's account. OpenAI says the company did not see the pair's work before it was published and did not access specific user data. However, the company cannot rule out that de-identified data from the pair's use of its products helped improve the models. Bubeck has posted messages that he says show he offered Buckmaster's team the chance to publish first. Altman wrote that Bubeck and the others acted with integrity and generosity.

Mathematician Terence Tao praised Buckmaster and Alpöge's result.

What does it mean?

Neither OpenAI's 100-page proof nor Buckmaster and Alpöge's work has been reviewed by independent outside mathematicians. The sources also do not fully agree on details, such as the number of agents and the time spent. It is therefore too early to say whether the problem has been solved, and who came first if so.