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Millennium Prize Problems

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Abstractions blog

What Makes the Hardest Equations in Physics So Difficult?

The Navier-Stokes equations describe simple, everyday phenomena, like water flowing from a garden hose, yet they provide a million-dollar mathematical challenge.

Simulation of Kelvin-Helmholz Instability
fluid dynamics

Mathematicians Find Wrinkle in Famed Fluid Equations

Two mathematicians prove that under certain extreme conditions, the Navier-Stokes equations output nonsense.

Submerged turbulent jet

A Fluid New Path in Grand Math Challenge

A daring speculation offers a potential way forward in one of the great unsolved problems of mathematics: the behavior of the Navier-Stokes equations for fluid flow.