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 ...

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 ...

Prime numbers just got less lonely. A proof announced this week claims to show that the number of primes with a near-neighbour that is also a prime number is infinite – although the “near-neighbour” ...

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 ...