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Four Colours Suffice: How the Map Problem Was Solved Paperback – 7 Aug 2003
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About the Author
Robin Wilson is Senior Lecturer in Mathematics at the Open University and Fellow of Keble College, Oxford.
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Top Customer Reviews
Unsurprisingly and understandably, Wilson slips up occasionally. Sometimes he doesn't give enough detail and explains obvious terms; often he presumes we understand more calculus than we do. For this reason, people with a very mathmatical brain and further education in mathmatics would find this book easier to cope with than other people just looking for a good read.
Wilson is every bit a mathmatician, which is noticeable in every aspect of the book. He writes in rather a scattered order: nearly every page talks about something "we will see later in Chapter X" or something "as we have already seen in Chapter X" and so the flow of the book is constantly disrupted. Because of the mathmatical aspect, the vocabulary used isn't exactly mind-blowing or particularly emotive. But then, if you want wonderful writing, you buy a novel.
That said, it is easy to see why this subject has excited mathmaticians past and present. One train of thought he didn't pursue (confusingly, to my mind) was that the pinicle of the book - the "solution" to the problem - may not be a solution at all. He talks of how other mathmaticians "solved" the problem in the past, and of how these solutions were disproved years later. In the case of Kempe, his solution was disproved a full eleven years after it was published. Given this information, and after learning of other mathmaticians rejection of the most recent "proof", I was surprised to read of Wilson's refusal to admit that this new solution may well be disproved in the future.
This is the kind of book, which urges you to grab a pen, paper and four coloured pencils, just to see if you can out-smart the world's best mathmaticians of the previous 150 years...
... and I'm still colouring...
Robin Wilson does an amazing job at describing the history of the four-colour theorem, from conception, through various attempts at proving it, past a few failed proofs (including Kempe's proof - which was only shown as defective over ten years after he published it), and onto Appel and Haken's proof. The thing that makes this book stand out from so many other 'light reading' mathematics books is the balance between biographical information and mathematics (the interesting stuff!). I would say that the majority of the book is maths-based, and the biographical content tends to be kept relevant to the 'storyline'.
You'll definitely want to be at least a little mathematically minded if you're going to enjoy this book - but, before long, you'll find it very easy to at least prove that five colours suffice... :)
Most Helpful Customer Reviews on Amazon.com (beta)
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.
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.
"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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