OpenAI claims a Navier-Stokes proof, and a mathematician cries foul

OpenAI said one of its unreleased models produced a complete proof of the Navier-Stokes existence and smoothness problem, one of the seven Millennium Prize problems that carry a $1 million bounty. The company put roughly $22.5 million of compute behind the effort. What turned the announcement into a fight is the timing. Tristan Buckmaster, a mathematician at NYU working with Levent Alpöge of Anthropic, had been closing in on the same result, and told TechCrunch that OpenAI started its run on September 1, right after word of his progress spread.

Buckmaster's objection is specific. The approach that worked, what he calls the route through a smooth force, was obscure enough that stumbling onto it independently within days strains belief. He also notes he had used OpenAI's Codex heavily while developing the argument, which raises the question of whether his own interactions fed a model that then reproduced the proof. He says the exchange got personal too, quoting OpenAI's Sébastien Bubeck asking "Why would you ruin your career?" OpenAI denies it saw any of the work before publication, saying it "did not see any of their work through any means until they released it publicly." The full account is in TechCrunch's report.

Why it matters

If you use coding or math assistants for original research, this is the concrete version of a worry that was abstract until now: your prompts may be training data, and a lab with more compute can finish a problem you opened. Read the credit and data-retention terms of the tools you rely on before you put novel work through them.