A type of chaos found in everything from prime numbers to turbulence can unify a pair of unrelated ideas, revealing a ...

One of the oldest and simplest problems in geometry has caught mathematicians off guard—and not for the first time. Since antiquity, artists and geometers have wondered how shapes can tile the entire ...

Arithmetic geometry is a vibrant field at the intersection of number theory and algebraic geometry, focussing on the study of polynomial equations and the distribution of their rational solutions.

A new approach has chipped away at a famously unsolved math problem. The Erdos-Turan conjecture in additive combinatorics is one of the longest lasting unsolved problems. The two mathematicians used ...

Hannah Cairo found herself stuck on a problem that wouldn’t leave her mind. It wasn’t a regular homework assignment—it was a decades-old mathematical puzzle believed to be true by leading experts in ...

A mathematician has solved a 30-year-old problem at the boundary between mathematics and computer science. He used an innovative, elegant proof that has his colleagues marveling at its simplicity. Hao ...

They made some progress, re-proving the conjecture in two dimensions using different techniques—ones they hoped would be applicable to the three-dimensional case. But then they hit a wall. “At some ...