Four Colors Suffice: How the Map Problem Was Solved - Revised Color Edition

Foreword by Ian Stewart xi Preface to the Revised Color Edition xiii Preface to the Original Edition xv 1 The Four-Color Problem 1 What 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 Examples 2 The Problem Is Posed 12 De Morgan Writes a Letter | Hotspur and the Athenaeum | Mobius and the Five Princes | Confusion Reigns 3 Euler's Famous Formula 28 Euler Writes a Letter | From Polyhedra to Maps | Only Five Neighbors | A Counting Formula 4 Cayley Revives the Problem ... 45 Cayley's Query | Knocking Down Dominoes | Minimal Criminals | The Six-Color Theorem 5 ... and Kempe Solves It 55 Sylvester's New Journal | Kempe's Paper | Kempe Chains | Some Variations | Back to Baltimore 6 A Chapter of Accidents 71 A Challenge for the Bishop | A Visit to Scotland | Cycling around Polyhedra | A Voyage around the World | Wee Planetoids 7 A Bombshell from Durham 86 Heawood's Map | A Salvage Operation | Coloring Empires | Maps on Bagels | Picking Up the Pieces 8 Crossing the Atlantic 105 Two Fundamental Ideas | Finding Unavoidable Sets | Finding Reducible Configurations | Coloring Diamonds | How Many Ways? 9 A New Dawn Breaks 124 Bagels and Traffic Cops | Heinrich Heesch | Wolfgang Haken | Enter the Computer | Coloring Horseshoes 10 Success! 139 A Heesch-Haken Partnership? | Kenneth Appel | Getting Down to Business | The Final Onslaught | A Race against Time | Aftermath 11 Is It a Proof? 157 Cool Reaction | What Is a Proof Today? | Meanwhile ... | A New Proof | Into the Next Millennium | The Future Chronology of Events 171 Notes and References 175 Glossary 187 Picture Credits 193 Index 195

Robin Wilson is emeritus professor of pure mathematics at the Open University and emeritus professor of geometry at Gresham College, London. He has written and edited many books on topics ranging from graph theory and combinatorics, via sudoku, philately, and the Gilbert and Sullivan operas, to the history of mathematics. He is currently president of the British Society for the History of Mathematics.

"The simplicity of the four-color conjecture is deceptive. Just how deceptive is made clear by Robin Wilson's delightful history of the quest to resolve it. . . . Four Colors Suffice is strewn with good anecdotes, and the author . . . proves himself skillful at making the mathematics accessible."--Jim Holt, New York Review of Books