What's that we hear? Sleigh bells! What's that we smell? Chestnuts roasting on an open fire! What can that mean? Christmas is coming! Celebrate the countdown with the Plus advent calendar featuring our favourite mathematical moments from 2012. Now, what's behind today's door...?

How many dimensions are there? In the latest online poll of our Science fiction, science fact project you told us that you'd like an answer to this question. So we asked theoretical physicist David Berman to find out more. We also bring you a range of other Plus articles exploring the question, as well as two articles from FQXi who are our partners on this project. Happy reading!

The Isaac Newton Institute celebrates its 20th birthday this year, having opened in July 1992. To join in the celebrations we bring you a selection of articles exploring some of the research programmes that have been held there. The Institute asked us to produce these articles in 2010 and we were honoured by being afforded this rare glimpse behind its venerable doors. And as you'll see, what started out as abstract mathematics scribbled on the back of a napkin can have major impact in the real world.

Does infinity exist? In the latest online poll of our Science fiction, science fact project you told us that you'd like an answer to this question. So we went to speak to cosmologist John D. Barrow to find out more. We also bring you a range of other Plus articles on the subject of infinity, as well as an article from FQXi who are our partners on this project. Happy reading!

Whether it's the planets moving around the Sun or building the perfect cycling track, the key to many questions in our lives lies in classical mechanics. This teacher package brings together all our content on mechanics.

This teacher package is devoted to the number line and the two major classes of numbers it's divided into: rational numbers, which can be written as fractions, and irrational numbers, which are everything else.

Stephen Hawking turned 70 in January 2012 and to celebrate, the University of Cambridge put on a scientific conference as well as a public symposium. Plus went along, of course, and here are the articles and podcast we have produced from the conferences. Happy reading and listening!

Is there such a thing as free will? In everyday life we all assume that there is: it's up to you whether you cheat in your tax return, and if you're caught, well then you deserve punishment. But when you look at it from a physics view point free will becomes a little tricky. Here's a collection of articles exploring free will.