The dangers of trading derivatives have been well-known ever since they were catapulted into the public eye by the spectacular losses of Nick Leeson and Barings Bank. **John Dickson** explains what derivatives are, and how they can be both risky, and used to reduce risk.

Sometimes a mathematical object can be so big that, however disorderly we make the object, areas of order are bound to emerge. **Imre Leader** looks at the colourful world of Ramsey Theory.

This pattern with kite-shaped tiles can be extended to cover any area, but however big we make it, the pattern never repeats itself. **Alison Boyle** investigates aperiodic tilings, which have had unexpected applications in describing new crystal structures.

**Bill Casselman** writes about the intriguing amateur mathematician Henry Perigal, who took his elegant proof of Pythagoras' Theorem literally to his grave - by having it carved on his tombstone.

*Plus* talks to **Christine Hogan**, programmer, sysadmin and author, now studying aerodynamics and hoping to become a member of a Formula One team.