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.

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 ...

Consider a pencil lying on your desk. Try to spin it around so that it points once in every direction, but make sure it sweeps over as little of the desk’s surface as possible. You might twirl the ...

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 ...

Math can sometimes seem like a bunch of confusing numbers and letters. But every once in a while, someone solves a puzzle that’s been around for decades—sometimes even over a hundred years! That’s ...

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 ...

Katie has a PhD in maths, specializing in the intersection of dynamical systems and number theory. She reports on topics from maths and history to society and animals. Katie has a PhD in maths, ...

The last dimension of Keller's conjecture has been proven using a computer algorithm. The conjecture involves the way hypercubes in different dimensions share sides when tiled. The proof is ...

A Rochester Institute of Technology doctoral student was part of a team of researchers that settled a 90-year-old math problem called Keller’s conjecture. David Narváez, who studies computing and ...