Kevin Hartnett

As topologists seek to classify shapes, the effort hinges on how to define a manifold and what it means for two of them to be equivalent.

A pair of mathematicians solved a legendary question about the proportion of vertices in a graph with an odd number of connections.

At 21, Ashwin Sah has produced a body of work that senior mathematicians say is nearly unprecedented for a college student.

For almost a century, the anonymous members of Nicolas Bourbaki have written books intended as pure expressions of mathematical thought.

Computer scientists are trying to build an AI system that can win a gold medal at the world’s premier math competition.

A powerful technique called SAT solving could work on the notorious Collatz conjecture. But it’s a long shot.

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

Herd immunity differs from place to place, and many factors influence how it’s calculated.

Representation theory was initially dismissed. Today, it’s central to much of mathematics.

Mathematicians try to figure out when problems can be solved using current knowledge—and when they have to chart a new path instead.