## Articles

**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.

**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.

*Plus*takes an illustrated tour of an extraordinary geometric construction: the

**Klein bottle**.

**number 23**.

**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.

**data compression**.

**Isaac Newton**and David Gregory - took place on the campus of Cambridge University. The discussion concerned the

**kissing problem**, but it was to be another 260 years before the problem was finally solved.

**Golden Ratio**, and ever since people have been fascinated by its extraordinary properties. Find out if beauty is in the eye of the beholder, and how the Golden Ratio crosses from mathematics to the arts.