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 ...

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.

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 ...

Prince Rupert of the Rhine first asked this question in the 17th century, and he soon found out the answer is yes. Later, ...

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 ...

Can you drill a hole in a cube that an identical cube could fall through? Prince Rupert of the Rhine first asked this ...

DeepMind’s AlphaEvolve helps solve a math puzzle with Terence Tao, showing how AI can now invent new ideas—and prove old ones ...

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 ...