A simple question about a spinning needle has haunted mathematicians for more than a century. It led to the Kakeya conjecture ...

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.

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 ...

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 Collatz Conjecture is a deceptively simple math problem. It has only two rules. First, pick any number. If it's even, divide it by two. If it's odd, multiply it by three and add one. This will ...

A mathematician has solved a 30-year-old problem at the boundary between mathematics and computer science. He used an innovative, elegant proof that has his colleagues marveling at its simplicity. Hao ...

Scientists recently announced progress on an elusive problem from 1960 known as the Sunflower Conjecture. While it doesn’t involve any plant biology, it does deal with objects called “mathematical ...