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# Mathematics

## 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.

## In Praise of Simple Problems

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

## Mathematicians Find Wrinkle in Famed Fluid Equations

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

## A Mathematician Who Decodes the Patterns Stamped Out by Life

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

## The (Math) Problem With Pentagons

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

## Mathematicians Crack the Cursed Curve

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.

## Secret Link Uncovered Between Pure Math and Physics

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

## A Physicist’s Physicist Ponders the Nature of Reality

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

## A Mathematician Who Dances to the Joys and Sorrows of Discovery

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