Erica Klarreich

The decades-old Sullivan’s conjecture, about the best way to minimize the surface area of a bubble cluster, was thought to be out of reach for three bubbles and up — until a new breakthrough result.

Richard Rusczyk, founder of Art of Problem Solving, has a vision for bringing “joyous, beautiful math” — and problem-solving — to classrooms everywhere.

On his way to winning a Fields Medal, James Maynard has cut a path through simple-sounding questions about prime numbers that have stumped mathematicians for centuries.

With her homeland mired in war, the sphere-packing number theorist Maryna Viazovska has become the second woman to win a Fields Medal in the award’s 86-year history.

Computer scientists can now solve a decades-old problem in practically the time it takes to write it down.

Cryptographers want to know which of five possible worlds we inhabit, which will reveal whether truly secure cryptography is even possible.

The existence of secure cryptography depends on one of the oldest questions in computational complexity.

A new paper shows how to create longer disordered strings than mathematicians had thought possible, proving that a well-known recent conjecture is “spectacularly wrong.”

Inside the symmetries of a crystal shape, a postdoctoral researcher has unearthed a counterexample to a basic conjecture about multiplicative inverses.