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.

Consider a pencil lying on your desk. Try to spin it around so that it points once in every direction, but make sure it sweeps over as little of the desk’s surface as possible. You might twirl the ...

Sam Raskin has wrapped his head around a math problem so complex it took five academic studies — and more than 900 pages — to solve. The results are a sweeping, game-changing math proof that was ...

Landmark results in geometry and number theory marked an exciting year for mathematics, at a time when advances in artificial intelligence are starting to transform the subject’s future. In May, a ...

A Japanese mathematician claims to have solved one of the most important problems in his field. The trouble is, hardly anyone can work out whether he's right. Sometime on the morning of 30 August 2012 ...