Kevin Hartnett

What’s a message, really? Claude Shannon recognized that the elemental ingredient is surprise.

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.