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Four Colors Suffice: How the Map Problem Was Solved 1st Edition

4.3 out of 5 stars 10 customer reviews
ISBN-13: 978-0691115337
ISBN-10: 0691115338
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Editorial Reviews

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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
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Review

"Wilson's lucid history weaves together lively anecdotes, biographical sketches, and a non-technical account of the mathematics."--Science



"An attractive and well-written account of the solution of the Four Color Problem. . . . It tells in simple terms an exciting story. It . . . give[s] the reader a view into the world of mathematicians, their ideas and methods, discussions, competitions, and ways of collaboration. As such it is warmly recommended."--Bjarne Toft, Notices of the American Mathematical Society



"A thoroughly accessible history of attempts to prove the four-color theorem. Wilson defines the problem and explains some of the methods used by those trying to solve it. His descriptions of the contributions made by dozens of dedicated, and often eccentric, mathematicians give a fascinating insight into how mathematics moves forward, and how approaches have changed over the past 50 years. . . . It's comforting to know that however indispensable computers become, there will always be a place for the delightfully eccentric mathematical mind. Let's hope that Robin Wilson continues to write about them."--Elizabeth Sourbut, New Scientist



"Recreational mathematicians will find Wilson's history of the conjecture an approachable mix of its technical and human aspects. . . . Wilson explains all with exemplary clarity and an accent on the eccentricities of the characters."--Booklist



"Robin Wilson appeals to the mathematical novice with an unassuming lucidity. It's thrilling to see great mathematicians fall for seductively simple proofs, then stumble on equally simple counter-examples. Or swallow their pride."--Jascha Hoffman, The Boston Globe



"Wilson gives a clear account of the proof . . . enlivened by historical tales."--Alastair Rae, Physics World



"Earlier books . . . relate some of the relevant history in their introductions, but they are primarily technical. In contrast, Four Colors Suffice is a blend of history anecdotes and mathematics. Mathematical arguments are presented in a clear, colloquial style, which flows gracefully."--Daniel S. Silver, American Scientist



"Wilson provides a lively narrative and good, easy-to-read arguments showing not only some of the victories but the defeats as well. . . . Even those with only a mild interest in coloring problems or graphs or topology will have fun reading this book. . . . [It is] entertaining, erudite and loaded with anecdotes."--G.L. Alexanderson, MAA Online

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Product Details

  • Hardcover: 280 pages
  • Publisher: Princeton University Press; 1 edition (January 26, 2003)
  • Language: English
  • ISBN-10: 0691115338
  • ISBN-13: 978-0691115337
  • Product Dimensions: 8.3 x 5.8 x 1.2 inches
  • Shipping Weight: 1 pounds
  • Average Customer Review: 4.3 out of 5 stars  See all reviews (10 customer reviews)
  • Amazon Best Sellers Rank: #1,754,922 in Books (See Top 100 in Books)

Customer Reviews

Top Customer Reviews

By Stephen Williams on April 14, 2008
Format: Hardcover
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.
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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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Format: Hardcover
I am a mathematician extensively familiar with the Four-Color Theorem and I was impressed by Wilson's book. He knows just what to put in and what to leave out; the narrative has just the right mixture of storytelling and math. If I have one complaint it is that the discharging procedure (part of the proof) is rather glanced over, but I can see how it would be daunting to expose "real" discharging procedures to a non-mathematical audience.

Overall, an entertaining and elegant book.
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Format: Paperback
Four Colors Suffice explains the history and some of the mathematics behind the four color theorem. While it goes into depth about it's history, there are chatty stories about the mathematicians, the book does not go into great depth about the mathematics involved. There are some mathematics, though, even some proofs. I consider this a good introduction to the four color theorem but it left me wanting more. I recommend this book for the story behind the four color theorem and also for a light introduction to the math but look elsewhere for an in depth discussion of the math.
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Format: Paperback
It's one of those great problems in math: easy for anyone to understand, baffling on the complexities of its solution, and unsolved for over a century. The question is: If you want to color a map so that countries with shared borders are different colors, how many colors do you need? What's the smallest number? A four year old can understand the question, but it took a fundamental revolution in mathematical proofs to state the answer with certainty: Four colors suffice.

This is a very readable history of the problem, from its phrasing in the mid-nineteenth century up to its mind-boggling proof in 1976, and a bit beyond that. It captures brief bits of the lives of the mathematicians who worked on it, as well as the furor over Appel and Haken's computer-based proof. Why was this so revolutionary? Because it was the first proof with steps that could never be checked by a human reader. Some people claimed the proof was incomplete until the programs were proven correct. Others stated that, if it couldn't be proven to a human mind, then nothing was really proven at all. Yet others objected to the proof's lack of mathematical elegance. It wasn't a scalpel that cut neatly to the heart of the problem, but a bulldozer hauled away huge buckets of potential counterexamples. A non-mathematician like me has to wonder: did this pave the way for acceptance of the 15,000-page "Classification theorem"? Although that theorem might not have been proven with computer assistance, its sheer mass is certainly similar.

The book does get a bit mathematical in places. The casual (and maybe not-so-casual) reader will be tempted to skip bits, and won't really lose the narrative thread by doing so. And, since the original proof is nearly 30 years old now, some of the excitement has worn off it.
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