Logic

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.

Two mathematicians have proved that two different infinities are equal in size, settling a long-standing question. Their proof rests on a surprising link between the sizes of infinities and the complexity of mathematical theories.

A surprising new proof is helping to connect the mathematics of infinity to the physical world.