OpenAI claims Navier–Stokes Millennium Prize solution (Lean-checked)

On 8 Sep 2026 OpenAI published “On the Navier–Stokes Millennium Prize Problem”: an internal model “significantly more capable than GPT‑6 Astra” allegedly shows smooth incompressible 3D Navier–Stokes with a smooth force can blow up in finite time while energy stays finite — Clay statements C and D — with a Lean formalization. OpenAI says training of the new model began 28 Aug; after 1 Sep Millennium rumors it spun up multi-agent groups (~10k concurrent for NS), used ~130B output tokens on NS (~300B across all attempted problems), found a resolution 5 Sep, and spent ~17h formalizing via GPT‑6 Astra. It does not claim the Clay prize. Concurrently NYU’s Tristan Buckmaster and Anthropic mathematician Levent Alpöge announced related Euler/NS progress and allege OpenAI started after learning of their approach; TechCrunch reports sharp exchanges with Sébastien Bubeck. OpenAI says it did not see their work before public release and notes the Euler cases differ (forced vs unforced). Terence Tao (via Simon Willison, 9 Sep) warned that open math problems are being “mined in a non-renewable fashion,” and that even rumors of work can trigger AI races that reverse open-science norms. The Verge (9 Sep) framed academia’s chill around OpenAI’s Millennium-style Navier–Stokes claim and the race dynamics around open math problems. The Verge (10 Sep) reports mathematician Andreas Thom accusing OpenAI of insufficient transparency on whether ChatGPT interactions entered training data after a non-sofic-groups result built on his and Gábor Kun’s work — echoing Tristan Buckmaster’s earlier Codex questions around the Navier–Stokes claim.