OpenAI AI agents solve Navier–Stokes Millennium Prize Problem in Lean
OpenAI published (Sept 8) “On the Navier–Stokes Millennium Prize Problem,” saying an internal multi-agent system—powered by a still-training model it calls significantly more capable than GPT-6 Astra—produced an analytical proof plus Lean formalization that smooth 3D incompressible Navier–Stokes flow can develop a finite-time singularity (Clay statements C and D), with finite energy throughout. Roughly 10,000 concurrent agents resolved Navier–Stokes in ~88 hours after a ~50-hour Euler (viscosity-zero) blow-up by ~100 agents; Lean verification took another ~17 hours via GPT-6 Astra. Across attempted Millennium-class problems agents sent ~4.9M messages / ~300B output tokens (~2.7M / ~130B on Navier–Stokes); OpenAI told New Scientist a customer rerun would cost ~$15M and said it will not claim the Clay $1M prize. OpenAI recognizes priority of Tristan Buckmaster (NYU) and Levent Alpöge (Anthropic) on forced Euler, denies accessing their Codex work or proofs, and notes its Euler result is unforced. Distinct from the Sept 6 research-acceleration intern metrics, An Alien Mind, Astra launch, and Anthropic’s Fermat Lean formalization.
