How understanding why something is impossible can often lead to deeper understanding, contemplations of philosophy and even new mathematics.

Yes, it does. And we have the maths to prove it.

What is infinity? Does it even exist? And how many infinities are there?

No one really knows the answer to this question. It's quite possible that there are more than one, in fact there may be infinitely many, popping in and out of existence like bubbles in a bubble bath.

Does time have a beginning? Is it possible to travel through time? And what does it mean to say that time is relative?

These articles introduce some of the question posed by the concept of information and its role in different areas of science and philosophy.

Can you measure information? It's a tricky question — but people have tried and come up with very interesting ideas.

In this year's advent calendar we bring you some of our favourite books and other mathematical toys, so you can surprise your friends and family or, even better, yourself!