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# partial differential equations

## Latest Articles

### To Test Einstein’s Equations, Poke a Black Hole

Two teams of researchers have made significant progress toward proving the black hole stability conjecture, a critical mathematical test of Einstein’s theory of general relativity.

### 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.

### Mathematicians Find Wrinkle in Famed Fluid Equations

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

### Yves Meyer, Wavelet Expert, Wins Abel Prize

The French mathematician was cited “for his pivotal role in the development of the mathematical theory of wavelets.”

### Famous Fluid Equations Are Incomplete

A 115-year effort to bridge the particle and fluid descriptions of nature has led mathematicians to an unexpected answer.

### In Noisy Equations, One Who Heard Music

Martin Hairer was named a 2014 Fields medalist for an epic masterpiece in stochastic analysis that colleagues say “created a whole world.”

### 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.