Customer Reviews

Four Colours Suffice

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This is the sort of book which all popularizers of Mathematics aspire to. It is well written, mathematically honest, with absolutely minimal prerequisites. On finishing the book, the reader should have a good understanding of the essentials of the Four Colour Problem, and its solution.

"Four Colours Suffice" is essentially a chronological history of the Four Colour Conjecture (4CC), the attempts to solve it, the successes and failures, the incremental and fundamental steps forward.

Although Wilson mentions that most of the 20th century used the graph theory perspective to attack the problem, he sticks with the map presentation throughout.

Wilson has a very readable style. He gives the reader a real sense of the key elements of the story, such as Kempe's chain argument, the necessity of pentagons in a minimal criminal (a minimal counterexample to the 4CC), discharging, and reducible and unavoidable configurations. He gives background on the main characters, with excellent photos, and is mostly kind in his evaluation of various individual's contributions. He calls Kempe's flawed proof an excellent proof, and is sincere in that characterization.

The book is very focussed on the 4CC, but does mention related issues such as Heawood's Theorem on the torus, and empires, and Birkhoff's chromatic polynomial. There are no exercises, but there are several proofs, e.g. the five colour theorem.

The controversy over Appel & Haken's proof closes out the book.

I was surprised at the number of people who were nipping at the heels of the 4CC when Appel & Haken announced their solution. There must have been some deflated egos amongst them, but all of the experts supported Appel & Haken when their proof was criticized for its reliance on computers, and its apparent ugliness.

One very minor disappointment is the lack of a bibliography, but this is nullified by the references scattered throughout the endnotes. This is not a math textbook, but is excellent supplementary/bedtime reading. Perhaps it will stimulate a young mathematician to present us with a readable, convincing, and surveyable proof of the 4CC. A Proof From The Book might be too much to hope for, but we can dream.

Every now and then a mathematical book of an historical/overview nature arrives on the scene and deserves to be an instant success.
"Four Colours Suffice" by Robin Wilson is precisely such a book.
This book marks the 150th anniversary of one of the most famous of all mathematical problems: How many colours are needed to colour in a map so that no two adjacent countries have the same colour?
The problem is famous for two main reasons:
(1) It is very simple to understand but incredibly difficult to solve.
(2) It was eventually solved in 1976 with computer assistance and represents the first major mathematical theorem which continues to resist any attmpet at a solution not requiring computer assitance.

The full story of how the proof finally came about has to rank as one of the most fascinating stories in the history of mathematics and Robin Wilson's account is full of interesting anecdotes and lots of humourous asides.
Wilson has gone to immense trouble to ensure that his book is both accurate and understandable to the novice. All in all a truly rewarding read for anyone with even a cursory interest in mathematics.

. . Ted Swart . .