Many mathematicians find the pure and tight patterns of juggling as irresistible as those of mathematics. Burkard Polster explains how to get to grips with the bewildering range of juggling possibilities and invites you to do your own virtual juggling.

On May 22nd 2009 the English Premier league had one more match day ahead. Taking up a challenge from the BBC radio, David Spiegelhalter and Yin-Lam Ng used statistics to predict the outcome of the last matches — and they were 90% correct. Find out how they did it.

A Gömböc is a strange thing. It looks like an egg with sharp edges, and when you put it down it starts wriggling and rolling around as if it were alive. Until quite recently, no-one knew whether Gömböcs even existed. Even now, Gábor Domokos, one of their discoverers, reckons that in some sense they barely exists at all. So what are Gömböcs and what makes them special?