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 biggest stories in science is quietly playing out in the world of abstract mathematics. Over the course of last year, researchers fulfilled a decades-old dream when they unveiled a proof of ...

May 5 -- It's not often that the abstract mathematical discipline of topology is in the news, but a respected British mathematician announced last month that he has proved a nearly century-old puzzle, ...

The first paper in a series of five claiming to prove the geometric Langlands conjecture, titled "Proof of the Geometric Langlands Conjecture I: Construction of the Functor," was published on May 6, ...

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 ...

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, ...

A conjecture in geometric probability about the asymptotic normality of the r-content of the r-simplex, whose r + 1 vertices are independently uniformly distributed random points of which p are in the ...