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.
This new edition features many color illustrations. It also includes a new foreword by Ian Stewart on the importance of the map problem and how it was solved.
About the Author
Table of Contents
Foreword by Ian Stewart xiPreface to the Revised Color Edition xiiiPreface to the Original Edition xv1The Four-Color Problem 1What Is the Four-Color Problem? | Why Is It Interesting? | Is It Important? | What Is Meant by "Solving" It? | Who Posed It, and How Was It Solved? | Painting by Numbers | Two Examples2The Problem Is Posed 12De Morgan Writes a Letter | Hotspur and the Athenaeum | Möbius and the Five Princes | Confusion Reigns3Euler's Famous Formula 28Euler Writes a Letter | From Polyhedra to Maps | Only Five Neighbors | A Counting Formula4Cayley Revives the Problem . . . 45Cayley's Query | Knocking Down Dominoes | Minimal Criminals | The Six-Color Theorem5. . . and Kempe Solves It 55Sylvester's New Journal | Kempe's Paper | Kempe Chains | Some Variations | Back to Baltimore6A Chapter of Accidents 71A Challenge for the Bishop | A Visit to Scotland | Cycling around Polyhedra | A Voyage around the World | Wee Planetoids7A Bombshell from Durham 86Heawood's Map | A Salvage Operation | Coloring Empires | Maps on Bagels | Picking Up the Pieces8Crossing the Atlantic 105Two Fundamental Ideas | Finding Unavoidable Sets | Finding Reducible Configurations | Coloring Diamonds | How Many Ways?9A New Dawn Breaks 124Bagels and Traffic Cops | Heinrich Heesch | Wolfgang Haken | Enter the Computer | Coloring Horseshoes10Success! 139A Heesch-Haken Partnership? | Kenneth Appel | Getting Down to Business | The Final Onslaught | A Race against Time | Aftermath11Is It a Proof? 157Cool Reaction | What Is a Proof Today? | Meanwhile . . . | A New Proof | Into the Next Millennium | The Future Chronology of Events 171Notes and References 175Glossary 187Picture Credits 193Index 195
What People are Saying About This
"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