The p-adics form an infinite collection of number systems based on prime numbers. They’re at the heart of modern number theory. The rational numbers are the most familiar numbers: 1, -5, ½, and every ...

WHILE experimenting with a system of counting by twelves, 1 suddenly I came upon a series of numbers that behaved in the most extraordinary way. Discovery followed discovery. One day the whole ...

Recent progress on the “sum product” problem recalls a celebrated mathematical result that revealed the power of miniature number systems. It’s one thing to turn a cartwheel in an open field. It’s ...