Four Colors Suffice: How the Map Problem Was Solved

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.

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.

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.

This is the sort of book which all popularizers of Mathematics aspire to. It is well written, mathematically honest, with absolutely minimal prerequisites. On finishing the book, the reader should have a good understanding of the essentials of the Four Colour Problem, and its solution."Four Colours Suffice" is essentially a chronological history of the Four Colour Conjecture (4CC), the attempts to solve it, the successes and failures, the incremental and fundamental steps forward.Although Wilson mentions that most of the 20th century used the graph theory perspective to attack the problem, he sticks with the map presentation throughout.Wilson has a very readable style. He gives the reader a real sense of the key elements of the story, such as Kempe's chain argument, the necessity of pentagons in a minimal criminal (a minimal counterexample to the 4CC), discharging, and reducible and unavoidable configurations. He gives background on the main characters, with excellent photos, and is mostly kind in his evaluation of various individual's contributions. He calls Kempe's flawed proof an excellent proof, and is sincere in that characterization.The book is very focussed on the 4CC, but does mention related issues such as Heawood's Theorem on the torus, and empires, and Birkhoff's chromatic polynomial. There are no exercises, but there are several proofs, e.g. the five colour theorem.The controversy over Appel & Haken's proof closes out the book.I was surprised at the number of people who were nipping at the heels of the 4CC when Appel & Haken announced their solution. There must have been some deflated egos amongst them, but all of the experts supported Appel & Haken when their proof was criticized for its reliance on computers, and its apparent ugliness. One very minor disappointment is the lack of a bibliography, but this is nullified by the references scattered throughout the endnotes. This is not a math textbook, but is excellent supplementary/bedtime reading. Perhaps it will stimulate a young mathematician to present us with a readable, convincing, and surveyable proof of the 4CC. A Proof From The Book might be too much to hope for, but we can dream.

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 . .