In the movies mathematicians are mostly mad. Since here at Plus we firmly believe in our sanity, we're puzzled as to why. So we charged Charlotte Mulcare with the unenviable task of sifting through five well-known maths movies and speculate towards an answer.

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.

You meet an old friend on holiday, you find your colleague shares your birthday, you win the lottery. Exactly how rare are these rare events? David Spiegelhalter investigates in his regular column on uncertainty and risk.

When the famous diagram fails

This issue's teacher package brings together all Plus articles on vectors and matrices, exploring anything from the maths of computer movies to climate change. It also has some handy links to related problems on our sister site NRICH.

It turns out your mum was wrong after all: you can judge a book by its cover. This book has a colourful, detailed, and tantalising cover adorned with portraits of people you may or may not know. Who are they, and what do they have to do with numbers at work, and the culture in which we live?

How do you do it? Horizontally from side to side, or perhaps criss-cross, producing a series of Xs running up your feet? Towards the end of The shoelace book, its author Burkard Polster raises a troubling question. Despite all the here-today, gone-tomorrow vagaries of fashion, and in spite of the huge variety of shoe styles available to us in this golden age of footwear, why does almost everyone lace their shoes in one of these two ways?

Ever wondered what mathematicians do all day? Finding Moonshine tells the story of a year in the life of the author, an Oxford professor known for his books, as well as radio and TV presentations of mathematics to the general public.