OpenAI announced a resolution to the Navier–Stokes existence and smoothness problem, one of seven $1,000,000 Millennium Prize Problems, using an unreleased internal model. The claim emerged amid accusations from Tristan Buckmaster, an NYU mathematics professor, and Levent Alpöge, a mathematician at Anthropic, who allege OpenAI may have accessed their work.

Buckmaster and Alpöge collaborated for nearly a year using Claude and Codex (mainly GPT-5.6 Sol), achieving a breakthrough on August 15. After rumors spread that Anthropic had solved a major problem, OpenAI launched its own effort on September 1, completing a Lean-verified proof by September 6 using GPT‑6 Astra. OpenAI's agents sent 2.7 million messages and used ~130 billion output tokens on Navier–Stokes alone.

OpenAI offered concurrent publication but excluded Alpöge due to competitive ties with Anthropic. Buckmaster questioned whether OpenAI's model trained on their Codex sessions; OpenAI denied accessing user data but acknowledged de-identified usage data might have improved models. Both proofs differ, notably on the Euler case (forced vs. unforced). The dispute highlights tensions around AI-assisted mathematical discovery and intellectual priority.