PANews|Sep 09, 2026 00:23
[OpenAI Publishes Solution to the Navier–Stokes Millennium Problem and Releases Lean Formal Proof]
OpenAI has announced that its internal system has provided a solution to the Navier–Stokes existence and smoothness problem: under smooth external forces, a three-dimensional incompressible fluid that is initially stationary and smooth can form a singularity within finite time, while maintaining finite energy throughout the entire process. OpenAI stated that this result corresponds to propositions C and D in the official statement from the Clay Mathematics Institute. The paper and Lean formal proof have been made publicly available, but the findings are still subject to independent review by the academic community. OpenAI revealed that the project utilized an internal model significantly more powerful than GPT-6 Astra, with approximately 10,000 parallel agents forming the proof within about 88 hours, sending 2.7 million messages and generating approximately 130 billion output tokens. The Lean formalization and verification took an additional 17 hours. OpenAI has no intention of claiming the Millennium Prize.
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