Probability

A decades-old proof showed that seven shuffles are enough to mix up a deck of cards. But it requires you to cut the deck with the precision of a professional magician. A new proof gets around that obstacle.

The central limit theorem started as a bar trick for 18th-century gamblers. Now scientists rely on it every day.

For decades, mathematicians have struggled to understand matrices that reflect both order and randomness, like those that model semiconductors. A new method could change that.

Turbulence is a notoriously difficult phenomenon to study. Mathematicians are now starting to untangle it at its smallest scales.

According to mathematical legend, Peter Sarnak and Noga Alon made a bet about optimal graphs in the late 1980s. They’ve now both been proved wrong.

The clearest picture yet of our “last universal common ancestor” suggests it was a relatively complex organism living 4.2 billion years ago, a time long considered too harsh for life to flourish.

It was intuitive, even obvious. It was also wrong.

The mathematician Daniel Litt has driven social media users to distraction with a series of simple-seeming but counterintuitive probability puzzles.

The French mathematician spent decades developing a set of tools now widely used for taming random processes.