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 ...

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 ...

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

The starting point for rigorous reasoning in mathematics is a system of axioms. An axiom is a statement that is assumed, without demonstration, to be true. It is usually self-evident, for example, ...

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 ...

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 ...

This is a preview. Log in through your library . Abstract The aim of this paper is two-fold. First, to give a direct proof for the already established result of Styer which states that a univalent ...