OpenAI says a 10,000-agent swarm solved Navier-Stokes, but can't rule out learning from a mathematician's private Codex sessions

OpenAI announced on September 8 that an unnamed internal model had solved the Navier-Stokes existence and smoothness problem, open for 26 years, using roughly 10,000 concurrent agents. The agents ran about 88 hours, exchanged 2.7 million messages and produced around 130 billion output tokens on Navier-Stokes alone; formalizing the proof in Lean took another 17 hours on GPT-6 Astra. At Astra's retail rate of $50 per million output tokens, those outputs alone price out near $6.5 million before any input tokens. Sam Altman asked on X whether the researchers knew the problem was "only worth $1 million," the size of the Clay prize. OpenAI says it does not intend to claim it.

The announcement shipped with a dispute attached. NYU mathematician Tristan Buckmaster and Anthropic researcher Levent Alpöge had been feeding unpublished drafts into private Codex sessions for closely related fluid-equation work. When OpenAI's Sébastien Bubeck texted that the company had proved "existence of forced blowup in R^3 and T^3," Buckmaster called the word "forced" a bright red flag, since smooth forcing was the obscure route the pair had been pursuing. OpenAI says no person or agent searched user data, then added that it "cannot rule out" that de-identified data derived from their use of its products helped improve its models. Buckmaster stopped short of alleging theft: "I do not know whether our data was used. I am not accusing anyone of anything." The project's origin was a rumor. Bubeck wrote that OpenAI "began working on the Millennium problems due to viral twitter rumors that Anthropic had resolved 2 Millenium problems." (VentureBeat)