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.

Sam Raskin in a still from the video “The Geometric Langlands Conjecture”. Credit: Institute for Advanced Study / Youtube Sam Raskin, a mathematician and professor at Yale University, has achieved a ...

It's all about the polynomials, baby. When you purchase through links on our site, we may earn an affiliate commission. Here’s how it works. Mathematicians have uncovered a big new piece of evidence ...

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 ...