Topology

Even as mathematicians and computer scientists proved big results in computational complexity, number theory and geometry, computers proved themselves increasingly indispensable in mathematics.

From crumpled paper to termite mounds to three-sided coins, L. Mahadevan has turned the whole world into his laboratory.

A small community of mathematicians is using a software program called Lean to build a new digital repository. They hope it represents the future of their field.

Mathematicians have long grappled with the reality that some problems just don’t have solutions.

Emily Riehl is rewriting the foundations of higher category theory while also working to make mathematics more inclusive.

Symplectic geometry is a relatively new field with implications for much of modern mathematics. Here’s what it’s all about.

While locked down due to COVID-19, Joshua Greene and Andrew Lobb figured out how to prove a version of the “rectangular peg problem.”

To distinguish between fundamentally different objects, mathematicians turn to invariants that encode the objects’ essential features.

It took Lisa Piccirillo less than a week to answer a long-standing question about a strange knot discovered over half a century ago by the legendary John Conway.