Logic

Number theorist Andrew Granville on what mathematics really is — and why objectivity is never quite within reach.

How hard is it to prove that problems are hard to solve? Meta-complexity theorists have been asking questions like this for decades. A string of recent results has started to deliver answers.

The numbers count a variety of seemingly unrelated mathematical structures.

Mathematicians predicted that if they imposed enough restrictions on how a shape might tile space, they could force a periodic pattern to emerge. But they were wrong.

Mathematicians using the computer program Lean have verified the accuracy of a difficult theorem at the cutting edge of research mathematics.

The goal of the “busy beaver” game is to find the longest-running computer program. Its pursuit has surprising connections to some of the most profound questions and concepts in mathematics.

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

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.

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