In May 2000, to inspire mathematicians and mark the start of the new millennium, the Clay Mathematics Institute in Cambridge, Massachusetts, launched its seven Millennium Prize Problems. Each challenge carried a $1 million award for a solution.
After OpenAI’s reported breakthrough on Navier–Stokes, the possibility of AI attacking multiple Millennium Prize Problems no longer sounds nonsense.
Rumors are now circulating that OpenAI is getting close to verifying a proof of the Hodge Conjecture, while OpenAI or Anthropic… pic.twitter.com/gAQT5GuQyv
— SciTech Era (@SciTechera) September 10, 2026
One of the seven challenges was the Navier-Stokes Equation. The Navier–Stokes equations are among the most useful mathematical tools for describing how fluids move (including liquids such as water and blood, and gases such as air). Their practical value is that they connect pressure, velocity, density, temperature, viscosity, and external forces, allowing scientists and engineers to predict or simulate flow.
Essentially, the Navier–Stokes equations express conservation of momentum for viscous fluids. The Navier–Stokes Millennium Prize Problem asked a very specific question: If you start with a perfectly smooth three-dimensional flow of an ordinary fluid, do the equations always keep producing a smooth, physically sensible flow forever, or can the flow become infinitely extreme at some finite time?
This week, OpenAI announced that it had solved the equation.
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