Four Colours Suffice: Amazon.ca: Robin Wilson: Books

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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

Book Description

A puzzlers delight for over a century, the four-colour problem was one of the most famous conundrums in mathematics, if not the most famous, and many thousands of puzzlers - amateur problem-solvers and professional mathematicians alike - have struggled to answer it. The problem is simply stated, and involves the colouring of maps: Can every map be coloured with no more than four colours so that neighbouring countries are coloured differently? First posed in 1852, it took more than 100 years of colouring maps and developing the necessary theoretical machinery before the result was established with certainty. Even then, difficult philosophical questions remained. Robin Wilson clarifies the problem, explains the proof and introduces the mathematicians behind the mathematics, among them a bishop, an astronomer, a botanist, an obsessive golfer and a bridegroom who spent his honeymoon colouring maps.

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First Sentence
Before we embark upon our historical journey, there are a number of basic questions to be answered. Read the first page

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5.0 out of 5 stars The Four Colour Problem,, Sep 22 2003

By

Testudinal Terpsichore (Dartmouth, Nova Scotia Canada) - See all my reviews

This review is from: Four Colours Suffice (Paperback)

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.

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5.0 out of 5 stars Four Colours Suffice, Nov 10 2002

By

Dr. Edward R. Swart (Kelowna, BC, Canada) - See all my reviews
(REAL NAME)

This review is from: Four Colours Suffice (Hardcover)

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 . .

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Amazon.com: 5.0 out of 5 stars (3 customer reviews)

27 of 27 people found the following review helpful

5.0 out of 5 stars Solved, April 14 2008

By Stephen Williams "Stephen Williams" - Published on Amazon.com

This review is from: Four Colours Suffice (Paperback)

Review of: "Four Colors Suffice - How the Map Problem Was Solved"

By: Robin Wilson

The four color map theorem is easy to understand and hard to prove.

The four color map theorem states that on a plane, which is divided into non-overlapping contiguous regions, the regions can be colored with four colors in such a way that all regions are colored and no two adjacent regions have the same color. In other words you can color any ordinary map with just four colors.

The proof of the four color theorem is very difficult. It is so difficult that the proof took over a century. The search for a proof was so long and became so complex that some mathematicians speculated that it was impossible. The four color served as one of the first real mathematical challenges posed to mathematics undergraduate students.

The statement of the challenge was deceptively simple. Prove that four colors are sufficient. The statement of the problem is so simple that it seems the solution should be equally simple. It is not simple. In 1976 the four-color theorem was finally demonstrated. The authors of the proof are Kenneth Appel and Wolfgang Haken of the University of Illinois.

The book "Four Colors Suffice" is the story of the century long search for the proof. The effort culminated in a computer program. Appel and Haken restated the problem as a collection of 1,936 types of maps. They had a computer program prove each of these 1,936 forms.

The author succeeds in conveying the excitement of the competition in those final months. This book shows the drama of one of the most exciting episodes of modern mathematics.

See also:

Graphs, Colourings and the Four-Colour Theorem (Oxford Science Publications)

The Four-Color Theorem: History, Topological Foundations, and Idea of Proof

Introduction to Graph Theory (4th Edition)

I thoroughly enjoyed this thoughtful and exciting book.

10 of 10 people found the following review helpful

5.0 out of 5 stars The Four Colour Problem,, Sep 22 2003

By Testudinal Terpsichore - Published on Amazon.com