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 ...

If pure math can teach us anything, it’s this: occasionally, your special interest might just change the world. For Joshua Zahl and Hong Wang, that special interest was the Kakeya conjecture. “I read ...

Fermat’s last theorem is just one of many examples of innocent-looking problems that can long stymie even the most astute mathematicians. It took about 350 years to prove Fermat’s scribbled conjecture ...

When Hannah Cairo started showing up at Berkeley Math Circle meetings as a teenager, nobody was betting she would topple a four-decade-old problem in harmonic analysis before she finished high school.

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 ...

Fermat’s last theorem is just one of many examples of innocent-looking problems that can long stymie even the most astute mathematicians. It took about 350 years to prove Fermat’s scribbled conjecture ...