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.

Monstrous moonshine, a quirky pattern of the monster group in theoretical math, has a shadow -- umbral moonshine. Mathematicians have now proved this insight, known as the Umbral Moonshine Conjecture, ...

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

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 ...