Four Colours Suffice: How the Map Problem Was Solved - Hardcover

Wilson, Robin

Hardcover

ISBN 10: 0713996706 ISBN 13: 9780713996708

Publisher: Allen Lane, 2002

Synopsis

The problem is simply stated, and involves the colouring of maps. Can every map be coloured with at most four colours so that neighbouring countries are coloured differently?

First posed 150 years ago, it took more than a century of colouring maps and developing the necessary theoretical machinery before the result was established with certainty. Even then, difficult philosophical questions remained.

With elegance and clarity, Robin Wilson explains the problem and the proof.

About this title

Review

At first glance Four Colours Suffice seems like such an easy thing to prove. However big and complicated the map, four colours are enough to distinguish each country from its neighbours. How do we prove that only four colours are needed? Once we realise that, if four countries all share borders with each other, then one country must be enclosed by the other three (try it), we seem to be most of the way there. But things turned out to be not quite so simple. Robin Wilson might balk at the idea that his sardonic and lively account of the problem and its solution is in any way farcical--as, indeed, might the dedicated mathematicians and keen amateurs whose 150 years of work he describes. But if the way an apparently simple problem throws out poisoned blossoms of complication, confusion and embarrassment is your definition of farce, then this story surely fits the bill. Proving the four-colour conjecture turned out to be heinously difficult, and has at last been achieved--and that in the ugliest way imaginable--only with the aid of a computer.

This, we can see now, was a landmark moment in mathematics: the moment we realised that there are proofs out there so complicated, that publishing them in full is impractical, working through them by hand is impossible, and explaining them to the public requires writers of a very special stamp indeed. (Robin Wilson, I should add, is most definitely one of them.) The publishers, in deciding to make a black-and-white book out of a colour problem, have not only done justice to Wilson's illustrations, but have also created one of the most visually arresting science books around. --Simon Ings

Review

"Wilson's lucid history weaves together lively anecdotes, biographical sketches, and a non-technical account of the mathematics."--Science

"An attractive and well-written account of the solution of the Four Color Problem. . . . It tells in simple terms an exciting story. It . . . give[s] the reader a view into the world of mathematicians, their ideas and methods, discussions, competitions, and ways of collaboration. As such it is warmly recommended."--Bjarne Toft, Notices of the American Mathematical Society

"A thoroughly accessible history of attempts to prove the four-color theorem. Wilson defines the problem and explains some of the methods used by those trying to solve it. His descriptions of the contributions made by dozens of dedicated, and often eccentric, mathematicians give a fascinating insight into how mathematics moves forward, and how approaches have changed over the past 50 years. . . . It's comforting to know that however indispensable computers become, there will always be a place for the delightfully eccentric mathematical mind. Let's hope that Robin Wilson continues to write about them."--Elizabeth Sourbut, New Scientist

"Recreational mathematicians will find Wilson's history of the conjecture an approachable mix of its technical and human aspects. . . . Wilson explains all with exemplary clarity and an accent on the eccentricities of the characters."--Booklist

"Robin Wilson appeals to the mathematical novice with an unassuming lucidity. It's thrilling to see great mathematicians fall for seductively simple proofs, then stumble on equally simple counter-examples. Or swallow their pride."--Jascha Hoffman, The Boston Globe

"Wilson gives a clear account of the proof . . . enlivened by historical tales."--Alastair Rae, Physics World

"Earlier books . . . relate some of the relevant history in their introductions, but they are primarily technical. In contrast, Four Colors Suffice is a blend of history anecdotes and mathematics. Mathematical arguments are presented in a clear, colloquial style, which flows gracefully."--Daniel S. Silver, American Scientist

"Wilson provides a lively narrative and good, easy-to-read arguments showing not only some of the victories but the defeats as well. . . . Even those with only a mild interest in coloring problems or graphs or topology will have fun reading this book. . . . [It is] entertaining, erudite and loaded with anecdotes."--G.L. Alexanderson, MAA Online

Edition details

• Publisher: Allen Lane
• Publication date: 2002
• ISBN 10: 0713996706
• ISBN 13: 9780713996708
• Binding: Hardcover
• Language: English
• Number of pages: 288