- 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 (View shipping rates and policies)
- Average Customer Review: 11 customer reviews
- Amazon Best Sellers Rank: #1,599,886 in Books (See Top 100 in Books)
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Four Colors Suffice: How the Map Problem Was Solved 1st Edition
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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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"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
Top customer reviews
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)
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Introduction to Graph Theory (4th Edition)
I thoroughly enjoyed this thoughtful and exciting book.
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. Even so, it's an enjoyable history of a problem that resisted attack for so long, and the remarkable attack that finally felled it.
And it leave me wondering: do my younger colleagues live in a world richer because of the radical solution, or poorer for the absence of such a wonderful mystery?