Most people probably don’t think of mathematics when they hear “busy beavers.” But these eager little animals symbolize one of the most amazing concepts of the knotty field: not everything can be ...

The original version of this story appeared in Quanta Magazine. All of modern mathematics is built on the foundation of set theory, the study of how to organize abstract collections of objects. But in ...

A basic feature of number theory, prime numbers are also a fundamental building block of computer science, from hashtables to cryptography. Everyone knows that a prime number is one that cannot be ...

Mathematical truths are often born of the conflict between order and disorder. Mathematicians discover patterns, and, to better understand the mysterious forces at play, they look for countervailing ...