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.

Katie has a PhD in maths, specializing in the intersection of dynamical systems and number theory. She reports on topics from maths and history to society and animals. Katie has a PhD in maths, ...

After German mathematician Gerd Faltings proved the Mordell conjecture in 1983, he was awarded the Fields Medal, often described as the “Nobel Prize of Mathematics.” The conjecture describes the set ...

A pair of mathematicians has solved the first chunk of one of the most famous conjectures about the additive properties of whole numbers. Proposed more than 60 years ago by the legendary Hungarian ...

Mathematical truths are often born of the conflict between order and disorder. Mathematicians discover patterns, and, to better understand the mysterious forces at play, they look for countervailing ...

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 ...

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 ...