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Millennium Prize Problems

Multimedia

The Map of Mathematics

February 13, 2020

Explore our surprisingly simple, absurdly ambitious and necessarily incomplete guide to the boundless mathematical universe.

Photo of smoke
Abstractions blog

What Makes the Hardest Equations in Physics So Difficult?

January 16, 2018

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

December 21, 2017

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

Submerged turbulent jet
Mathematics

A Fluid New Path in Grand Math Challenge

February 24, 2014

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.