AI TRENDS | OpenAI Says AI System Generated Navier-Stokes Proof, Pending Mathematical Review

OpenAI said an internal AI system generated a proof for the Navier-Stokes equations, claiming it constructed a case in which a three-dimensional incompressible fluid develops a singularity in finite time. According to Sina Finance, the proof also includes a Lean formalization, but it has not yet undergone long-term peer review or received formal recognition from the Clay Mathematics Institute. The paper, titled "Finite Time Blowup for Navier-Stokes," follows the finite-time singularity path. OpenAI said the AI system built a fluid that starts from rest and is acted on by a smooth external force, with its velocity becoming unbounded in finite time while the total energy remains finite. OpenAI said about 10,000 parallel AI agents took part in the proof search over 88 hours, exchanging nearly 5 million messages. Another model then spent about 17 hours formalizing the result into a Lean proof, and OpenAI researchers estimated the computing cost at several million dollars. The company said the work was prompted after it learned that other researchers might have made related progress. It also said the Navier-Stokes proof was completed independently by its internal system, while acknowledging that its research direction was inspired by related rumors and that it could not fully rule out user data having been used in de-identified form to improve the model. OpenAI said it does not plan to claim the $1 million prize. It added that even if the proof passes independent review, the main significance would be in AI development, as the model moves from retrieving and organizing existing knowledge toward solving open problems, long-horizon collaboration, and formal verification.