OpenAI said on Tuesday that an unreleased internal model, running roughly 10,000 AI agents over 88 hours, produced a proof tied to the Navier-Stokes existence and smoothness problem, one of seven Millennium Prize Problems the Clay Mathematics Institute has offered $1 million for since 2000. The equations describe how fluids move, and they sit at the center of turbulence, something physicists still don’t fully understand.
According to OpenAI, the effort started on September 1, after researchers heard rumours that two Millennium Prize problems had recently been cracked. In response, they turned their newest model, described as “significantly more capable” than the company’s GPT-6 Astra release, loose on the problems that remained. By September 5, the agents had exchanged nearly 3 million messages.
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
The effort burned through 300 billion output tokens, roughly $22.5 million in compute at current rates. OpenAI says it isn’t going after the Millennium Prize itself, and while the proof was certified using the programming language Lean, it hasn’t been independently verified or accepted by the Clay Institute yet.
Well, OpenAI has made its announcement. But a separate dispute over who deserves credit has emerged since the announcement.
Is “Solved” doing more work than the proof actually supports?
Most headlines flattened “existence and smoothness problem” into “solved,” but the problem has two possible answers, and they’re not the same achievement.
For 90 years, mathematicians have tried to figure out whether the three-dimensional Navier-Stokes equations always behave, producing smooth, well-defined solutions, or whether under the right starting conditions they can “blow up,” meaning a fluid’s speed shoots to infinity at some finite point in time. That can’t happen in the real world, but it can happen on paper.
Scientific American’s reporting confirms OpenAI’s claim goes toward the second answer: a proof that the equations can develop a singularity in finite time. Either answer technically resolves the Millennium Problem, but proving things fall apart under specific conditions is a different kind of claim than proving they never do, and that distinction is exactly what mathematicians will pick apart once the full proof is public. Lean certification means the logical steps hold together internally. It doesn’t mean the framing or the assumptions behind it are right, and only peer review can settle that.
The more interesting story is what happened to two human mathematicians
NYU mathematician Tristan Buckmaster and Anthropic researcher Levent Alpöge had spent close to a year chasing a related proof using large language models, including Claude and OpenAI’s own Codex.
On August 15, they published Lean-verified proofs of finite-time blow-up for three related fluid systems, a serious result on its own. Buckmaster says OpenAI found out about their unpublished work within the week that followed, and that Sébastien Bubeck, who runs OpenAI’s math team, then offered him a choice: either let OpenAI announce a full solution the next day and credit the pair as “the closest humans to the problem,” or publish his own paper first, but only if Alpöge’s name came off it, because OpenAI reportedly didn’t want the Anthropic affiliation attached.
Buckmaster says he refused and was told, “Why would you ruin your career?” OpenAI has since said neither its researchers nor its agents saw any of the pair’s work before it was made public, though the company acknowledged it “cannot rule out” that de-identified data from their product usage played some role.
Whichever account turns out to be accurate, the argument itself says something the “AI solves 90-year math problem” headline doesn’t say. Mathematicians are now doing serious original research inside tools built and hosted by the same companies racing to publish results first. If a mathematician’s unpublished work passes through an AI company’s own tools, that same company may end up positioned to see it and to publish first. For Buckmaster and Alpöge, what’s at stake isn’t the prize money, OpenAI has already said it isn’t pursuing that. It’s whether the two of them get recognized as the mathematicians who actually got there.
FAQs
What math problem did OpenAI say it solved?
OpenAI said an internal AI model produced a proof related to the Navier-Stokes existence and smoothness problem, one of seven Millennium Prize Problems established by the Clay Mathematics Institute in 2000. The equations describe fluid motion and sit at the center of turbulence.
Has OpenAI’s proof been independently verified?
No. The proof has been certified using the programming language Lean, which checks that the logical steps are internally consistent, but it has not been reviewed or accepted by the Clay Mathematics Institute or independently verified by outside mathematicians.
What is the dispute between OpenAI and NYU mathematician Tristan Buckmaster?>
Buckmaster and Anthropic researcher Levent Alpöge had spent close to a year working toward a related proof using large language models. Buckmaster alleges OpenAI learned of their unpublished work and moved to publish a competing result first, offering him credit only under certain conditions. OpenAI says neither its researchers nor its AI agents saw the pair’s work before it was made public.
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