OpenAI's AI solved Navier-Stokes — and a mathematician cries foul
A Millennium Prize problem fell today, and the fight over who solved it is arguably bigger news than the proof. OpenAI published an AI-generated solution to the Navier–Stokes existence and smoothness problem. Hours earlier, the NYU mathematician whose work it raced posted a statement accusing the lab of finding out about his approach and throwing a data center at it.
OpenAI says an unreleased internal model — "significantly more capable than GPT-6 Astra" — produced a proof that smooth 3D fluid flow can develop a singularity in finite time, settling statement C (and D) of the Clay Mathematics Institute's official formulation. The company began training the model on August 28, launched a multi-agent attack on all open Millennium problems on September 1 after hearing rumors two had fallen, and got its answer on September 5 — about 88 hours after the first agents spun up, with 17 more hours of Lean formalization by GPT-6 Astra. The winning group ran on the order of 10,000 concurrent agents, and the whole effort burned 4.9 million agent messages and roughly 300 billion output tokens; TechCrunch pegged that at about $22.5 million at current Astra rates, while OpenAI research head Mark Chen told reporters only that it cost "in the millions." OpenAI says it does not intend to claim the $1 million prize.
The shape of the result matters as much as the result: it's a vortex that spirals inward and stretches like spaghetti, speeding up as its core shrinks while total energy stays finite — the equations break down on their own, with a smooth external force, rather than being handed an infinite one. Along the way the agents also resolved the unforced Euler regularity problem, a related blowup question, with about 100 agents working 50 hours. For scale on how fast this curve is moving, we covered the same lab's earlier record run in OpenAI's Astra cuts the bounded prime gap record to 186 — that was one problem, one record, and a rounding error next to this.
The foul is about process, not priority. Tristan Buckmaster and Levent Alpöge — an NYU professor and an Anthropic researcher working on their own time — posted three finite-time blowup results on Monday and say information about their progress reached OpenAI before it was public. Buckmaster writes that OpenAI's first prompt went out "in the past few days, after information about our work had reached OpenAI," and that the route OpenAI took — a smooth force, options C and D in Fefferman's statement — is the one he and Alpöge had "quietly chosen to attack," one that "almost nobody else I know of was working on." He also alleges Sebastien Bubeck asked him to publish without Alpöge's name and, when he resisted, replied "Why would you ruin your career?" and "If you don't want me to be nice, then I don't have to be nice." Because the pair leaned heavily on Codex, Buckmaster wants answers about whether his logs fed the model.
OpenAI denies seeing their work. Bubeck says he came in "with the best possible intentions" and never asked for Alpöge to be dropped from his own paper; Sam Altman posted that the team "acted with integrity and generosity throughout." The company's own writeup, though, leaves a door open: "while unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models." That sentence is the one every enterprise customer will read.
What to watch: whether the Clay Mathematics Institute or a third-party Lean audit weighs in, and whether labs write a binding rule against racing users' private work before the next prize falls.
If your unpublished work lives in a frontier lab's chat logs, who owns the discovery it enables? Tell us in the comments.
