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 ...

Author: David Simmons (GitHub: davsim1) This is a program to find examples or counterexamples of Beal's Conjecture. It uses a brute force approach to do this by looping through all of the ...

Abstract: We prove some structure results for transversely reducible Sasaki manifolds. In particular, we show a Sasaki manifold with positive Ricci curvature is transversely irreducible, and so join ...

Abstract: We consider products of matrix exponentials under the assumption that the matrices span a nilpotent Lie algebra. In 1995, Leonid Gurvits conjectured that nilpotency implies that these ...

(Phys.org)—A group of mathematicians specializing in arithmetic geometry met for five days earlier this month in an attempt to understand a proof constructed by Shinichi Mochizuki, of Kyoto University ...

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 ...