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Four Colors Suffice: How the Map Problem Was Solved Hardcover – 2003


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Product Details

  • Hardcover
  • Publisher: Princeton University Press (2003)
  • Language: English
  • ISBN-10: 0691115338
  • ISBN-13: 978-0691115337
  • Product Dimensions: 21.1 x 14.6 x 2.9 cm
  • Shipping Weight: 476 g
  • Average Customer Review: 4.4 out of 5 stars  See all reviews (5 customer reviews)
  • Amazon Bestsellers Rank: #1,631,908 in Books (See Top 100 in Books)

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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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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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Format: Hardcover
The history of the four color problem is one that illuminates much of what makes mathematics such a great topic to explore and was the first instance of a whole new movement in mathematics. It started with a letter from Augustus De Morgan in 1852, where he asks a question that was first asked of him by a student.
"What is the least possible number of colors needed to fill in any map (real or invented) so that neighboring countries are always colored differently?"
This apparently simple question was not immediately resolved, and over the years there were many attempts to answer it. In 1879, Alfred Bray Kempe published what was thought to be a proof that four colors were enough, but it turned out that the proof was flawed. It was only when the problem was reduced to a set of special cases that could be examined by a computer that a conclusive "proof" was finally derived by a computer in 1976. Kenneth Appel and Wolfgang Haken, who have been given credit for resolving the problem, programmed the computer. Many mathematicians found this type of proof very unnerving, and it forced the mathematical community to reexamine what the definition of a mathematical proof really is.
This story, told very well by Robin Wilson, has student input, progress that proceeds in fits and starts with one major false proof, reduction of the problem to simpler terms based on new ideas and different approaches to the problem and the unprecedented proof of a major result by computer analysis. It also demonstrates how persistent the mathematical community can be when confronted with an unsolved problem. As befits the topics, Wilson relies heavily on diagrams to get his points across, which is a necessity.
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Format: Hardcover
One of the most famous theorems in mathematics is the Four Color Map Theorem. It is wonderfully simple to understand, and interesting to spend time doodling on. Mapmakers like to take a map like, say, the states of the U.S. and color in the states with different colors so they are easily told apart; the theorem states that any such map (or any imaginary map of contiguous regions), no matter how complex, only requires four colors so that no state touches a state of the same color. This is not obvious, but if you try to draw blobs on a sheet of paper that need more than four colors (in other words, five blobs each of which touches all the others along a boundary), you will quickly see that the theorem seems to be true. In fact, ever since the question was mentioned, first in 1852, people have tried to draw maps that needed five colors, many of them very complicated, but no one succeeded. But that isn't good enough for mathematics; it's interesting that no one could do it, but can it be proved that it cannot be done? For over a century, there was no counter-example and yet no proof, but in 1976 there was a proof that has held up, but is controversial because it used a computer. The amazing story of the years of competition and cooperation that finally proved the theorem is told in _Four Colors Suffice: How the Map Problem Was Solved_ (Princeton) by Robin Wilson. This is as clear an explanation of the problem, and the attempts to solve it, as non-mathematicians are going to get, and best of all, it is an account, exciting at times, of the triumphs and frustrations along the way, not just with the final proof, but in all the years leading up to it.
Surprisingly, mapmakers aren't very interested in the problem.
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