John Barrow gives us an overview, from Aristotle's ideas to Cantor's never-ending tower of mathematical infinities, and from shock waves to black holes.

We all take for granted that mathematics can be used to describe the world, but when you think about it this fact is rather stunning. This article explores what the applicability of maths says about the various branches of mathematical philosophy.

Many people like mathematics because it gives definite answers. Things are either true or false, and true things seem true in a very fundamental way. But it's not quite like that. You can actually build different versions of maths in which statements are true or false depending on your preference. So is maths just a game in which we choose the rules to suit our purpose? Or is there a "correct" set of rules to use? We find out with the mathematician Hugh Woodin.

David Spiegelhalter explains that waiting for an infinite number of monkeys to produce the complete works of Shakespeare is not just a probabilistic certainty, it also gives us an insight into how long we can expect to wait for a rare event to happen.

What's the nature of infinity? Are all infinities the same? And what happens if you've got infinitely many infinities? In this article Richard Elwes explores how these questions brought triumph to one man and ruin to another, ventures to the limits of mathematics and finds that, with infinity, you're spoilt for choice.
Richard Elwes continues his investigation into Cantor and Cohen's work. He investigates the continuum hypothesis, the question that caused Cantor so much grief.
Peter Macgregor explores the beautiful world of the infinite.
The maths of infinite series

Infinities are tricky things and have perplexed mathematicians and philosophers for thousands of years.

Eugen Jost is a Swiss artist whose work is strongly influenced by mathematics. He sent us this Postcard from Italy, telling us about his work and the important roles that nature and numbers play in it.