Navier–Stokes Equations
A system of partial differential equations describing the motion of viscous fluids. The question of the existence and smoothness of their solutions is one of the seven Millennium Prize Problems established by the Clay Mathematics Institute, carrying a one-million-dollar award.
Timeline (last 90 days)
On September 8, 2025, New York University mathematician Tristan Buckmaster publicly released three AI-assisted research results on fluid equations, and in a four-page statement disclosed that OpenAI researchers told him their internal model had generated a finite-time blow-up proof for the Navier-Stokes equations with smooth external force.
The finite-time blow-up proof for the Navier-Stokes equations allegedly generated by OpenAI's internal model is approximately 100 pages long, and if correct and satisfying all conditions of the Clay Mathematics Institute's grand prize, it could potentially address a Millennium Prize Problem carrying a $1 million reward.
The route involving external forces corresponds to options C and D in the formal statement of the Clay Prize problem.
All Facts (3)
The finite-time blow-up proof for the Navier-Stokes equations allegedly generated by OpenAI's internal model is approximately 100 pages long, and if correct and satisfying all conditions of the Clay Mathematics Institute's grand prize, it could potentially address a Millennium Prize Problem carrying a $1 million reward.
50%UnverifiedThe route involving external forces corresponds to options C and D in the formal statement of the Clay Prize problem.
50%UnverifiedOn September 8, 2025, New York University mathematician Tristan Buckmaster publicly released three AI-assisted research results on fluid equations, and in a four-page statement disclosed that OpenAI researchers told him their internal model had generated a finite-time blow-up proof for the Navier-Stokes equations with smooth external force.
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