OpenAI says one of its internal models produced a proof for the Navier–Stokes problem. That is one of the Millennium Prize problems, long unsolved in mathematics. The proof shows three-dimensional fluid equations can break down in finite time. OpenAI describes the model as far more capable than its GPT-6 Astra system. The company says the work began on 1 September, after staff heard rumours that rivals were close. NYU mathematician Tristan Buckmaster and Anthropic researcher Levent Alpöge had related unpublished work. Buckmaster questioned whether OpenAI drew on their research direction or private material. He also alleged an OpenAI researcher pushed to drop Alpöge from authorship over his employer. OpenAI denies accessing their user data but cannot rule out an indirect link. It says it does not train on enterprise inputs, and personal accounts can opt out.

• cost in the millions of dollars
• roughly 10,000 agents used
• $1 million prize not claimed
• effort began Sept. 1