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

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

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

A mathematician who has analyzed card shuffling for decades is tackling one final nemesis: “smooshing.”

A collaboration between mechanical engineers and mathematicians has revealed universal rules for how wrinkles form.

Surprising oil drop experiments suggest that the quantum world may not be as strange as advertised.

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.

By investigating the central role played by knots in fluids and fields, physicists hope to unravel long-standing mysteries of turbulence.

New data collected by mathematicians and oceanographers in the frigid waters of the Southern Ocean could dramatically improve climate models.