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On October 23, 1852, Professor Augustus De Morgan wrote a letter to a colleague, unaware that he was launching one of the most famous mathematical conundrums in history--one that would confound thousands of puzzlers for more than a century. This is the amazing story of how the "map problem" was solved.
The problem posed in the letter came from a former student: What is the least possible number of colors needed to fill in any map (real or invented) so that neighboring counties are always colored differently? This deceptively simple question was of minimal interest to cartographers, who saw little need to limit how many colors they used. But the problem set off a frenzy among professional mathematicians and amateur problem solvers, among them Lewis Carroll, an astronomer, a botanist, an obsessive golfer, the Bishop of London, a man who set his watch only once a year, a California traffic cop, and a bridegroom who spent his honeymoon coloring maps. In their pursuit of the solution, mathematicians painted maps on doughnuts and horseshoes and played with patterned soccer balls and the great rhombicuboctahedron.
It would be more than one hundred years (and countless colored maps) later before the result was finally established. Even then, difficult questions remained, and the intricate solution--which involved no fewer than 1,200 hours of computer time--was greeted with as much dismay as enthusiasm.
Providing a clear and elegant explanation of the problem and the proof, Robin Wilson tells how a seemingly innocuous question baffled great minds and stimulated exciting mathematics with far-flung applications. This is the entertaining story of those who failed to prove, and those who ultimately did prove, that four colors do indeed suffice to color any map.
- Sales Rank: #1589730 in Books
- Brand: Brand: Princeton University Press
- Published on: 2003-01-26
- Original language: English
- Number of items: 1
- Dimensions: 1.16" h x 5.76" w x 8.30" l,
- Binding: Hardcover
- 280 pages
- Used Book in Good Condition
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
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
From the Inside Flap
"I loved Robin Wilson's book on the four color problem, because it gives the history as well as the arguments. The history is presented so entertainingly, and the arguments so lucidly, that I'm sure the book will find a large audience, and delight any audience as much as it did me."--John Conway
"An intriguing historical account of one of the most baffling enigmas in mathematics: the Four Color Theorem. Robin Wilson provides fascinating insights into how mathematicians think, and shows that questions that are simple to ask may not be simple to answer."--Ian Stewart
"Robin Wilson has combined a complete history of the approach that led to the solution of the four color problem with a description of the techniques involved that can be read with pleasure and comprehension by undergraduates as well as professional mathematicians."--Kenneth Appel, University of New Hampshire
Most helpful customer reviews
35 of 36 people found the following review helpful.
Solved
By Stephen Williams
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.
See also:
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.
15 of 16 people found the following review helpful.
light reading but informative
By Patrick Regan
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.
11 of 13 people found the following review helpful.
Four Colours Suffice
By Dr. Edward R. Swart
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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