Probability

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.

Four mathematicians have estimated the chances that there’s a clear path through a random maze.

If Anna beats Benji in a game and Benji beats Carl, will Anna beat Carl?

Just as ice melts to water, graphs undergo phase transitions. Two mathematicians showed that they can pinpoint such transitions by examining only local structure.