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 ...

The twin primes conjecture is one of the most important and difficult questions in mathematics. Two mathematicians have solved a parallel version of the problem for small number systems.

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.