Calculus is a collection of tools, such as differentiation and integration, for solving problems in mathematics which involve "rates of change" and "areas". In the first of two articles aimed specially at students meeting calculus for the first time, Chris Sangwin tells us about these tools - without doubt, the some of the most important in all of mathematics.

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.

Human beings are famously prone to error, and proof-readers are, after all, only human. But who picks up the errors a proof-reader misses? John D. Barrow challenges readers to estimate the errors that aren't found from the errors that are.

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.

If you had a crystal ball that allowed you to see your future, what would you arrange differently about your finances? Plus talks to the Government Actuary, Chris Daykin about the pensions crisis, and how actuaries use statistical and modelling techniques to plan for all our futures.

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.