Episode one of Another Five Numbers, the BBC radio series presented by Simon Singh.

Simon Singh's journey begins with the number 4, which for over a century has fuelled one of the most elusive problems in mathematics: is it true that any map can be coloured with just 4 colours so that no two neighbouring countries have the same colour? This question has tested some of the most imaginative minds — including Lewis Carroll's — and the eventual solution has aided the design of some of the world's most complex air and road networks.