Kevin Hartnett

Even with no one in charge, army ants work collectively to build bridges out of their bodies. New research reveals the simple rules that lead to such complex group behavior.

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.

A new version of AlphaGo needed no human instruction to figure out how to clobber the best Go player in the world—itself.

Voevodsky’s friends remember him as constitutionally unable to compromise on the truth—a quality that led him to produce some of the most important mathematics of the 20th century.

The color of LED lights is controlled by a clumsy process. A new mathematical discovery may make it easier for us to get the hues we want.

It’s “a definitive study for all time, like writing the final book,” says one researcher who’s mapping out new classes of geometric structures.

Big advances in math can happen when mathematicians move ideas into areas where they seem like they shouldn’t belong.

Paul Erdős placed small bounties on hundreds of unsolved math problems. Over the past 20 years, only a handful have been claimed.

To avoid garbled messages, mathematicians might translate them into geometric form.

Ramsey’s theorem predicts a surprising (and useful) consistency in the organization of graphs. Here’s a simple visual proof of how it works.