Mathematics is often about uncovering patterns. For example, certain areas of topology revolve around categorizing knots or geometric shapes, and number theory explores properties such as the ...

A shard of smooth bone etched with irregular marks dating back 20,000 years puzzled archaeologists until they noticed something unique – the etchings, lines like tally marks, may have represented ...

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 ...

Hilbert’s 12th problem asked for novel analogues of the roots of unity, the building blocks for certain number systems. Now, over 100 years later, two mathematicians have produced them. Problems in ...