Four Colours Suffice: How the map problem was solved by Robin Wilson, Allen Lane/Penguin, 拢12.99, ISBN 0713996706 Reviewed by Elizabeth Sourbut
IT SEEMED a simple enough proposition: in 1852 mathematician Francis Guthrie noticed that on a map of England, you only need four colours to ensure that no two adjacent counties are the same hue. He suggested that this was true for any map drawn on a plane surface. But the proof of this simple conjecture turned out to be highly elusive, and the problem captured the imaginations of amateurs and professionals alike over the following century.
It wasn鈥檛 until 1976 that an alliance of three mathematicians and a computer finally produced a proof hundreds of pages long. And there are still arguments about whether a proof that cannot be entirely checked by hand constitutes a proof at all.
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Robin Wilson celebrates the 150th anniversary of Guthrie鈥檚 observation with Four Colours Suffice, a thoroughly accessible history of attempts to prove the four-colour 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 150 years.
But that final proof by Kenneth Appel, Wolfgang Haken and John Koch raised interesting philosophical questions about what constitutes a mathematical proof. When it was finally published in 1977, mathematicians divided along age lines. Those over 40 refused to accept the computer-generated sections, while those under 40 were more suspicious of the lengthy hand calculations. Wilson concludes that computer-assisted proofs are here to stay. They may lack elegance, but the necessary calculations are just too long and complex to be reliably worked through by hand.
Meanwhile, mathematicians have moved on to a whole series of even more difficult problems related to the theorem. It鈥檚 comforting to know that however indispensable computers become, there will always be a place for the delightfully eccentric mathematical mind. Let鈥檚 hope that Robin Wilson continues to write about them.