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 ...

In an old Indian parable, six blind men each touch a different part of an elephant. They disagree about what the elephant must look like: Is it smooth or rough? Is it like a snake (so thinks the man ...

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 ...

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 ...