It’s an educated guess, not a proof. But a good conjecture will guide math forward, pointing the way into the mathematical unknown. Mountain climbing is a beloved metaphor for mathematical research.

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.

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

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 ...

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 ...

At the 1994 reception for the prestigious Kyoto Prize, awarded for achievements that contribute to humanity, the French mathematician André Weil turned to his fellow honoree, the film director Akira ...

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 ...

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 ...