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 ...

The grandest project in mathematics has received a rare gift, in the form of a mammoth 350-page paper posted in February that will change the way researchers around the world investigate some of the ...

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, ...