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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.

The mathematician Richard Schwartz finds the hidden depth lurking in simple mathematical puzzles.

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

Corina Tarnita deciphers bizarre patterns in the soil created by competing life-forms.

Triangles fit effortlessly together, as do squares. When it comes to pentagons, what gives?

A famously difficult mathematical problem resisted solution for over 40 years. Mathematicians have finally resolved it by following an intuition that links number theory to physics.

An eminent mathematician reveals that his advances in the study of millennia-old mathematical questions owe to concepts derived from physics.

Edward Witten reflects on the meaning of dualities in physics and math, emergent space-time, and the pursuit of a complete description of nature.

Federico Ardila opens up about his journey as a mathematician, teacher, Colombian transplant, DJ and creator of mathematical spaces.