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September 8, 2026
OpenAI’s Navier–Stokes Claim Sparks a Fight Over Who Got There First
OpenAI portrays its result as a remarkable demonstration of frontier AI, insisting it neither accessed outside researchers’ work nor copied their proof. Buckmaster sees a troubling imbalance instead: a tool provider with enormous computing power may have turned customers’ private research progress into a competitive edge.
OpenAI’s announcement began with an audacious claim: an internal system had produced both an analytical proof and a Lean formalization showing that smooth three-dimensional fluid motion can develop a finite-time singularity — a proposed resolution of the Navier–Stokes Millennium Prize problem, open for roughly 90 years.1
The company says it started training its new model on August 28. On September 1, after hearing rumors that two Millennium problems had been solved, it launched coordinating agent groups against the remaining problems. Roughly 10,000 agents ultimately worked on Navier–Stokes; OpenAI says they reached a result on September 5, after 88 hours, amid an effort consuming about 300 billion output tokens.1 Sam Altman called watching it unfold “one of the most amazing moments” in OpenAI’s history.
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But the triumph collided with work already underway. On the eve of OpenAI’s announcement, NYU’s Tristan Buckmaster and Anthropic mathematician Levent Alpöge released findings on the related forced Euler problem. Buckmaster says they had quietly pursued a rare route involving a smooth force — and that word of their progress reached OpenAI while they were finalizing their results.3
His central concern is not merely priority. Buckmaster and Alpöge had used Codex and Claude in their research, and Buckmaster questioned whether private Codex interactions could have informed the model. “It is not the direction one arrives at in a few days by giving a model the problem statement,” he wrote of the approach OpenAI also took.3 He further alleged that OpenAI’s Sébastien Bubeck urged him to remove Alpöge’s credit and, when Buckmaster considered going public, said: “Why would you ruin your career?”3
OpenAI disputes the implication. It says neither its researchers nor agents saw the pair’s work before publication and that “no specific user data was accessed.” Yet it acknowledges it cannot entirely exclude the possibility that de-identified product data improved its models, while arguing the two proofs — and their Euler results — differ materially.1 Altman has defended the team’s conduct as marked by “integrity and generosity,” saying OpenAI initially sought a joint release.4
The unresolved issue now reaches beyond one theorem: whether scientists can trust AI labs to be collaborators without becoming rivals armed with vastly deeper compute.