The Kakeya conjecture predicts how much room you need to point a line in every direction. In one number system after another — with one important exception — mathematicians have been proving it true.

Many complicated advances in research mathematics are spurred by a desire to understand some of the simplest questions about numbers. How are prime numbers distributed in the integers? Are there ...

The Babylonians used separate combinations of two symbols to represent every single number from 1 to 59. That sounds pretty confusing, doesn’t it? Our decimal system seems simple by comparison, with ...