OpenAI has published a blog post claiming its internal agents resolved the Navier–Stokes existence and smoothness problem, one of the seven Millennium Prize Problems. The resolution was achieved approximately 88 hours after the team launched the effort on September 1st, following rumors that mathematicians Tristan Buckmaster and Levent Alpöge had also found a solution.
- OpenAI's agents sent 2.7 million messages and used approximately 130 billion output tokens to resolve the Navier–Stokes problem.
- Lean formalization and verification took an additional 17 hours via GPT‑6 Astra.
- The total effort across all attempted problems involved 4.9 million messages and about 300 billion output tokens.
- OpenAI stated it did not access specific user data from Buckmaster and Alpöge but could not rule out that de-identified data improved their models.
The article highlights the ethical implications of AI labs potentially using customer data to improve models, raising concerns about whether such training might inadvertently help competitors solve problems first.