NYU mathematician Tristan Buckmaster announced three proofs with a preliminary finding on the Navier-Stokes smoothness problem. He worked with Levent Alpoge, a mathematician employed by Anthropic, using OpenAI's Codex and Claude. Shortly afterwards OpenAI published a full proof of the same problem. OpenAI credits an unreleased next-generation model and says the week-long effort used vast amounts of computing power. Buckmaster says information about his unpublished progress reached OpenAI before his work was public. He says OpenAI began prompting only days later, along a route almost nobody else pursued. He also alleges OpenAI's Sebastien Bubeck asked him to drop Alpoge's credit and warned him about his career. OpenAI says it saw none of their work and that the two proofs differ. It cannot rule out that de-identified usage data helped train its models. Buckmaster raised the separate worry that his own Codex sessions fed OpenAI's effort; users can opt out of such training.

• 300 billion output tokens used
• $22.5M of compute at Astra rates
• $1M Millennium Prize bounty
• OpenAI effort began 1 September