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.

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 ...

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 ...

In August 2012, Shinichi Mochizuki, Japanese mathematician from Kyoto University’s Research Institute for Mathematical Sciences, posted four papers on his website that claimed to contain a proof of ...

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 ...