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 second of two articles aimed specially at students meeting calculus for the first time, Chris Sangwin tells us how to move on from first principles to differentiation as we know and love it!

Following on from his article 'The prime number lottery' in last issue of Plus, Marcus du Sautoy continues his exploration of the greatest unsolved problem of mathematics: The Riemann Hypothesis.

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.

Combinatorial Game Theory is a powerful tool for analysing mathematical games. Lewis Dartnell explains how the technique can be used to analyse games such as Twentyone and Nim, and even some chess endgames.

Not only are paper models of geometric shapes beautiful and intriguing, but they also allow us to visualise and understand some important geometric constructions. Konrad Polthier tells us about the gentle art of paper folding.

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.

Marcus du Sautoy begins a two part exploration of the greatest unsolved problem of mathematics: The Riemann Hypothesis. In the first part, we find out how the German mathematician Gauss, aged only 15, discovered the dice that Nature used to chose the primes.

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.