Overview
- OpenAI announced that a private, non-public model produced a proposed proof of the Navier–Stokes existence and smoothness problem using about 10,000 collaborating AI agents over roughly 88 hours and that GPT-6 Astra completed a Lean formal verification in about 17 hours; the company said it will not seek the Clay Mathematics Institute prize.
- OpenAI described the result as showing a smooth, initially stationary fluid can develop a finite-time singularity under externally forced smooth conditions corresponding to cases C and D of the official problem statement, a technical claim that requires community vetting.
- Several mathematicians and rival researchers, including Tristan Buckmaster and Levent Alpöge, questioned the timing and raised concerns that research stored in OpenAI’s Codex could have influenced the result; OpenAI denied impropriety while acknowledging it cannot rule out improvements from anonymized product data.
- The announcement has immediate operational effects: Astra demand is described as unprecedented and OpenAI may pause new Pro subscriptions to protect existing users, the company cut Luna’s price by 80% to drive usage, and executives say they used AI in an internal chip design tape-out called Jalapeno; outside estimates put compute costs for the work in the tens of millions of dollars.
- The episode has intensified safety and governance concerns after recent researcher resignations and prior model incidents, prompting calls for clearer provenance, independent verification of the proof, and new rules for how high-capability, non-public models are tested and released.