On Tuesday OpenAI published a proof for a problem mathematicians have been chewing on since the 1960s. The Navier-Stokes equations describe how fluids and gases move, and the open question was whether a flow that starts out smooth stays smooth forever. It doesn’t. A smooth fluid at rest can develop a singularity in finite time — a vortex spiralling inward, stretching longer and longer, with finite energy throughout.
That settles statements C and D of the official Millennium formulation. The Clay Institute pays a million dollars per problem, seven in total. OpenAI says plainly it does not intend to claim it.
How it was done
The numbers are the part that stops you. Starting September 1, a group of around 10,000 concurrent agents ran on an internal model OpenAI describes as significantly more capable than GPT-6 Astra. 88 hours of runtime, 2.7 million messages between agents, roughly 130 billion output tokens. Formalizing the result in Lean took another 17 hours; the code is on GitHub.
No preprint, no peer review queue — a machine-checked proof. That’s the second story buried in this one, and arguably the bigger one. Formal verification kills the question “did anyone actually check this?” before it gets asked.
Then it got ugly
Tristan Buckmaster of NYU had announced his own results just before midnight on September 7, together with Levent Alpöge. OpenAI’s post followed twelve hours later. Buckmaster claims OpenAI only hit the accelerator after word of his progress leaked. The heavier accusation is the second one: OpenAI researcher Sébastien Bubeck allegedly pushed to leave Alpöge off the author list because he works at Anthropic. Buckmaster quotes him as saying, “Why would you ruin your career?”
Sam Altman pushes back: “Now that we can see their work, the approaches appear to be different.” OpenAI does concede it launched the effort after hearing rumors that competitors had solved major math problems — and that it cannot fully rule out that de-identified training data from the two researchers’ own tool usage helped indirectly.
Charles Fefferman of Princeton, for what it’s worth, points somewhere else entirely for credit: to Diego Córdoba and Luis Martínez-Zoroa, whose earlier work the whole thing rests on.
What actually bothers me
Terence Tao put his finger on it last night on Mathstodon: “We have now seen that even the rumor of someone working on a problem can trigger a massive amount of AI-powered effort to flatten it before the original research project has time to reach its full potential.”
That’s no longer a maths problem. It’s an incentive problem. Think out loud about an interesting open question and you risk a lab showing up with ten thousand agents. The rational response is to stop talking. Which would be a shame, since research has run the other way for centuries.
And the uncomfortable question stays on the table: should a lab that sells researchers their tools be racing those same researchers to the same results?
Sources: OpenAI: On the Navier–Stokes Millennium Prize Problem, Quanta Magazine, Axios: OpenAI’s historic math solution overshadowed by credit controversy, Simon Willison, Terence Tao on Mathstodon