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.

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 ...

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 ...

When you purchase through links on our site, we may earn an affiliate commission. Here’s how it works. A mathematician has solved a 30-year-old problem at the boundary between mathematics and computer ...

Since the conjecture was already known to be true in one and two dimensions, they sought to prove it in three: to show that if you can shift copies of one shape to tile all of three-dimensional space, ...