## Articles

**Winner of the general public category**. Enormous is the right word: this theorem's proof spans over 10,000 pages in 500 journal articles and no-one today understands all its details. So what does the theorem say?

**Richard Elwes**has a short and sweet introduction.

Learn about the aerodynamics of footballs and perfect your free kick.

What goes up must come down — or does it? Find out how to cheat gravity with

**Julian Havil**.**Robert L. Devaney**explores the maths behind these beauties and shows that they're loaded with mathematical meaning.

**Colva Roney-Dougal**takes us into their abstract world and puzzles over a game of Solitaire.

*Mir*and sent it hurtling through space. As NASA astronaut

**Michael Foale**tells

*Plus*, the fate of

*Mir*and its crew hinged on a classical set of equations.

**Yutaka Nishiyama**explains why, and how beautiful mathematical oddities can inspire us to discover new mathematics.