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Four Colors Suffice: How the Map Problem Was Solved Paperback – Nov 7 2004

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Four Colors Suffice: How the Map Problem Was Solved
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Product Details

  • Paperback: 280 pages
  • Publisher: Princeton University Press (Nov. 7 2004)
  • Language: English
  • ISBN-10: 0691120234
  • ISBN-13: 978-0691120232
  • Product Dimensions: 20.8 x 13.9 x 1.8 cm
  • Shipping Weight: 322 g
  • Average Customer Review: 4.5 out of 5 stars  See all reviews (6 customer reviews)
  • Amazon Bestsellers Rank: #1,214,467 in Books (See Top 100 in Books)
  • See Complete Table of Contents

Product Description

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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 --This text refers to the Hardcover edition.

From Booklist

The four-color conjecture, formulated in 1852, was among the most popular unsolved problems in mathematics. Amateurs and professionals alike succumbed to its allure. It is, simply stated: four colors are all that is needed to fill in any map so that neighboring countries are always colored differently. That the proof, which was completed in 1976, consumed a thousand pages and gobs of computer time hints at the hidden complexity encountered by those attempting to solve it. Recreational mathematicians will find Wilson's history of the conjecture an approachable mix of its technical and human aspects, in part because the math involved is understandable even to able middle-schoolers. The conjecture seemed a snap to its originator, one Francis Guthrie, but his claimed proof has never surfaced; those proofs that did surface, prior to the final breakthrough by Kenneth Appel and Wolfgang Haken, contained fatal errors. Wilson explains all with exemplary clarity and an accent on the eccentricities of the characters, Lewis Carroll among them. Gilbert Taylor
Copyright © American Library Association. All rights reserved --This text refers to the Hardcover edition.

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First Sentence
Solving any type of puzzle, such as a jigsaw or crossword puzzle, can be enjoyed purely for relaxation and recreation, and certainly the four-colour problem has provided many hours of enjoyment - and frustration - for many people. Read the first page
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Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
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2 of 2 people found the following review helpful By Dr. Edward R. Swart on Nov. 10 2002
Format: Hardcover Verified Purchase
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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Format: Hardcover
This book deserves every star it gets from me! The quality of the writing startled me since afterall it was written by a mathematician. The four color problem was presented in a fascinating manner. Brief histories on the people who worked on the problem were very interesting and added flavor. Also, the book was not dry. It had nice anecdotes and a sense of humor ("humour"-see below). Diagrams and formulas were presented in a very clear concise manner to anyone who has a good geometrical foundation or higher.
My nitpicky thoughts that would probably never bother anyone else:
The title is deceptive. "Colors" is spelled "colour" in the actual text.
Also, the example of the shape of football was used in the text. What he meant was a soccerball. Completely different shapes come to mind.
My last nitpicky thing is on the same British/American culture line of reasoning. Apparently the Brit's use a term called "overleaf" I finally realized that he meant "on the next page" about half way through. Other than the regional differences in language, the work was presented beautifully. I plan on looking for anything else Mr. Wilson has written. I've always loved math but never really liked reading about it. This book has definitely sparked an interest in reading more like this!
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Format: Hardcover
I enjoyed this book very much - it is fresh in expression and introducing complex ideas - even humourous at times! And yet for all that there is a sense of some lack of achievement also, although this may not be a failing of Mr Wilson.
As a mathematics student - and I have studied quite a lot of mathematics - it seems to me that proofs came in three kinds. There are the mind opening 'obvious' ones that are so stand-alone that once you read them there is nothing to learn. The blinkers have been lifted from the eyes and the world is a different place. Then there are the proofs that take such a lot of work to assimilate and for a long time you just don't see it. Perhaps you never really do, but you do come to accept it because the mathematics community is convinced. Then there are the proofs that even the mathematics community struggle with. The four-colour problem's proof is one of these. Consequently there is left a nagging doubt, which I gather is quite widespread amongst people far wiser and knowledgeable than me - than Mr Wilson also I suspect.
The curious thing is that a conjecture like the four-colour mapping, or Fermat's last theorem, or the conjecture that all even numbers can be made up of the sum of two prime numbers, is so powerful AND there are no counter examples available to challenge the conjecture. So why can they not be proved by some elegant insight such as Fermat claimed for his last theorem but never showed the world before his immanent death in a duel? Why can the four-colour problem only be proved by such inelegant computer-assisted means as this book describes? Perhaps Mr Wilson's greatest achievement is in exposing the doubts and dissatisfactions of the current proof of the four-colour problem despite the appearance that it may well be adequate (this goes for the proof of Fermat's last theorem too).
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