On 23 October 1852, Professor Augustus De Morgan sat down to write a letter to a colleague, unaware that it marked the beginning of one of the most famous and controversial conundrums in mathematics - one that would take thousands of puzzlers over a century to answer. This is the story of how it was solved.
The problem posed in the letter came from one of De Morgan's former students and involved the colouring of maps. It asked: what is the least possible number of colours needed to fill in any map (real or invented), so that neighbouring countries are always coloured differently? It sounded simple, yet amateur problem-solvers and professional mathematicians alike were to spend years colouring maps and developing the necessary theoretical machinery before the result could be established with certainty. Even then, difficult questions remained, and the solution, which involved 1,200 hours of computer time, was surrounded by suspicion and scorn.
Here Robin Wilson clarifies the problem, explains the proof, introduces the characters behind the mathematics - among them a bishop, an astronomer, a botanist, an obsessive golfer and a bridegroom who spent his honeymoon colouring maps - and shows how they all connect with patterns on footballs, maps on doughnuts and the great rhombicuboctahedron.
Press contact: Sarah Christie 020 7010 4989 / sarah.christie@penguin.co.uk
Four Colours Suffice
- patterns, maps, footballs and why four colours are all you need
By Robin Wilson
Published by Allen Lane on 7th November 2002, £12.99
On 23rd October 1852, Professor Augustus De Morgan sat down to write a letter to a colleague. What, he asked, is the least number of colours needed to colour any map, real or invented, so that neighbouring countries are always coloured differently? He was unaware that this question, an intellectual challenge of enormous complexity, marked the beginning of one of the most famous conundrums in mathematics - one that would take thousands of puzzlers over a century to solve and would include characters as diverse as Lewis Carroll, the Bishop of London, a professor of French Literature, an April Fool hoaxer, a botanist who loved heathers, a mathematician who loved golf, a bridegroom who spent his honeymoon colouring maps, a man who set his watch just once a year, and a Californian traffic cop.
Robin Wilson has been fascinated for many years by the four-colour problem and he tells its entertaining story in Four Colours Suffice. More than a century of colouring maps and developing the necessary theoretical machinery was to pass after the problem was first posed before the fact that four colours suffice for all possible patterns was proven. Published to coincide with the 150th anniversary of the problem and 25 years after the proof was published, Four Colours Suffice tells the history of the problem and the many people, mathematicians and enthusiastic amateurs alike, who attempted to solve it, as well as those who finally did. But was it really a genuine and veritable proof?
Kenneth Appel and Wolfgang Haken's eventual and hard-won solution, which involved 1,200 hours of computer time, nearly 10 years' work, and their five children to help finish it, was greeted with great enthusiasm, scepticism and concern about the use of the computer. But can the proof be considered valid if it cannot be checked by hand? What are the implications of using computers to solve mathematical problems? In Four Colours Suffice, Robin Wilson shows how the problem connects with maps on doughnuts and horseshoes, patterns on footballs, and the great rhombicuboctahedron, but only one question remains: has the problem really been solved?
Robin Wilson is Senior Lecturer in Mathematics at the Open University and Fellow of Keble College, Oxford and formerly Visiting Professor in the History of Mathematics at Gresham College, London. He will be exploring the four-colour problem at Gresham College, London on Monday 21st October, The Mathematics Institute, Oxford on Tuesday 22nd October and at The London Mathematical Society on Wednesday 23rd October - the 150th anniversary of the problem. Wolfgang Haken and Kenneth Appel will be in the UK in the week of publication.
