Mike Yates looks at the life and work of wartime code-breaker Alan Turing. Find out what types of numbers we can't count and why there are limits on what can be achieved with Turing machines.

"Nothing is more interesting than nothing" - or so says Ian Stewart, Professor of Mathematics at Warwick University. Many people have difficulty with the concept of zero. In fact, it has only really been used for the last 1500 years or so.

Since we first wrote about the Goldbach Conjecture we've had many requests for more information about  it and about how our Goldbach calculator works. We answer some of your questions here but the Goldbach conjecture touches on a strange area of maths that may leave you even more curious than before...

Mathematics is a maze, according to Ian Stewart at the Royal Institutions Christmas Lecture.

New technology has provided us with some amazing images - satellite images, medical images, even images beamed back from Mars. Julian Stander tells us about the increasing role of statistics in interpreting them.

In his second article, David Henwood explains the role of mathematics in the design of Hi-Fi loudspeakers.

Coincidences are familiar to us all but what are the so-called laws of chance? From coin tossing to freak weather events, Geoffrey Grimmett explains how probability is at the heart of it all.

• What's in a name?
• Disaster

We know there is infinitely many primes, but are there infinitely many twin primes?