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.

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.

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

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.

Can Dan Goldston and Cem Yalcin Yildrim repair the hole in their proof to make the biggest breakthrough in prime number theory for 80 years?

The Riemann Hypothesis is probably the hardest unsolved problem in all of mathematics, and one of the most important. It has to do with prime numbers - the building blocks of arithmetic. Nick Mee, together with Sir Arthur C. Clarke, tells us about the patterns hiding inside numbers.

To study a system, mathematicians begin by identifying its most crucial elements, and try to describe them in simple mathematical terms. As Phil Wilson tells us, this simplification is the essence of mathematical modelling.

One million dollars is waiting to be won by anyone who can solve one of the grand mathematical challenges of the 21st century. In the second of two articles, Chris Budd looks at the well-posedness of the Navier-Stokes equations.