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 ...

The Latin root of the word conjecture, conicere, means to throw things together. Think of Jackson Pollock splashing different paints onto a canvas and hoping for some kind of coherent result. In ...

A mathematical problem more than 300 years old gets a formal proof with the help of computer formal verification. A team led by mathematician Thomas Hales has delivered a formal proof of the Kepler ...

In early 20th-century Paris, there was a boy so mesmerized by math that when his parents took his paper and pencil away, urging him to play, he found a rock and scribbled algebra equations on the ...

Chinese mathematician Wang Hong has solved an “infamous” geometry problem called the Kakeya conjecture within three dimensions. It is considered a breakthrough that could have implications for imaging ...

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 ...