Logic

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.

AI tools are shaping next-generation theorem provers, and with them the relationship between math and machine.

The dendritic arms of some human neurons can perform logic operations that once seemed to require whole neural networks.

Decades after the landmark proof of Fermat’s Last Theorem, ideas abound for how to make it even more reliable. But such efforts reflect a deep misunderstanding of what makes the proof so important.