OpenAI provides solution to Navier–Stokes existence and smoothness problem using internal AI agents
OpenAI announced a solution to the Navier–Stokes existence and smoothness problem, a prominent Millennium Prize Problem that has remained unresolved for approximately 90 years. The solution, produced by an internal system of coordinating agents powered by a model more capable than GPT‑6 Astra, demonstrates that an initially smooth fluid at rest can develop a singularity in finite time. This result establishes statement "C" and "D" in the official Millennium Prize formulation. The system utilized approximately 10,000 concurrent agents to discover a vortex that spirals inward and speeds up until its velocity grows without bound while its energy remains finite. The proof was verified using Lean, a tool for formalizing mathematical proofs. OpenAI stated that it will not claim the $1 million Millennium Prize for this achievement. The announcement follows a closely related advance by Tristan Buckmaster and Levent Alpöge, who solved the forced Euler problem. While OpenAI denies that its agents had direct access to the work of Buckmaster and Alpöge, the company acknowledged that de-identified data from their products may have helped improve its models. The resolution of the Navier–Stokes problem is part of a broader trend of AI-driven mathematical discoveries, which has prompted discussions among mathematicians regarding the role of human researchers in an AI-dominated field.
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On the Navier–Stokes Millennium Prize Problem
OpenAI
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If AI can do math, what’s the point of mathematicians?
Scientific American