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 ...

The Collatz conjecture is also known as the “3n + 1” problem. It’s an easy problem to explain and check, and has been tested up into the nineteen figure range. But it’s only now that anyone has come ...

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 team of mathematicians has solved a math problem first posed more than 40 years ago. It took three mathematicians almost 15 years to solve the famous Rota’s Conjecture – a theory first posed by ...

The artificial intelligence (AI) program DeepMind has gotten closer to proving a math conjecture that's bedeviled mathematicians for decades and revealed another new conjecture that may unravel how ...

Hannah Cairo found herself stuck on a problem that wouldn’t leave her mind. It wasn’t a regular homework assignment—it was a decades-old mathematical puzzle believed to be true by leading experts in ...

Caroline Klivans, senior lecturer in applied mathematics and computer science, achieved every student’s dream and proved her former advisor wrong. The Partitionability Conjecture was postulated by ...

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 ...