Kevin Hartnett

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.

19th-century mathematicians thought the “roots of unity” were the key to solving Fermat’s Last Theorem. Then they discovered a fatal flaw.

The simple Möbius strip illustrates a deep mathematical challenge that has long tormented the field of symplectic geometry.

The ancient study of an object’s curvature is guiding mathematicians toward a new understanding of simple equations.

Can you turn a two-dimensional fractal into a 3-D object? Break out your scissors and tape for a chance to win a 3-D printed sculpture.

How do physicists reconstruct what really happened in a particle collision? Through calculations that are so challenging that, in some cases, they simply can’t be done. Yet.