In the first of a new series 'Imaging Maths', Plus takes an illustrated tour of an extraordinary geometric construction: the Klein bottle.

The 2003 Dirac Lecturer, distinguished physicist Freeman Dyson, tells Plus why he is an optimist, what makes life interesting and why old-fashioned maths is what you need for physics.

The number chosen by the England captain for his Real Madrid shirt is rich in mysterious connotations. But mathematician Marcus du Sautoy backs a new theory to explain why Beckham has plumped for number 23.

All of science can be regarded as motivated by the search for rules behind the randomness of nature, and attempts to make prediction in the presence of uncertainty. Chris Budd describes the search for pattern and order in chaos.

Wen Quek works for an award-winning architectural cooperative based in London. Recently, she worked on the new library at the University of Cambridge's Centre for Mathematical Sciences. As she tells Plus, Wen sees many parallels between mathematics and architecture.