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Four Colors Suffice
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Preface xi 1. The four-colour problem 1 WHAT IS THE FOUR-COLOUR 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 16 DE MORGAN WRITES A LETTER | HOTSPUR AND THE ATHENAEUM | MOBIUS AND THE FIVE PRINCES | CONFUSION REIGNS 3. Euler's famous formula 38 EULER WRITES A LETTER | FROM POLYHEDRA TO MAPS | ONLY FIVE NEIGHBOURS | A COUNTING FORMULA 4. Cayley revives the problem ... 60 CAYLEY'S QUERY | KNOCKING DOWN DOMINOES | MINIMAL CRIMINALS | THE SIX-COLOUR THEOREM 5. ... and Kempe solves it 73 SYLVESTER'S NEW JOURNAL | KEMPE'S PAPER | KEMPE CHAINS | SOME VARIATIONS | BACK TO BALTIMORE 6. A chapter of accidents 95 A CHALLENGE FOR THE BISHOP | A VISIT TO SCOTLAND | CYCLING AROUND POLYHEDRA | A VOYAGE AROUND THE WORLD | WEE PLANETOIDS 7. A bombshell from Durham 116 HEAWOOD'S MAP | A SALVAGE OPERATION | COLOURING EMPIRES | MAPS ON DOUGHNUTS | PICKING UP THE PIECES 8. Crossing the Atlantic 143 TWO FUNDAMENTAL IDEAS | FINDING UNAVOIDABLE SETS | FINDING REDUCIBLE CONFIGURATIONS | COLOURING DIAMONDS | HOW MANY WAYS? 9. A new dawn breaks 169 DOUGHNUTS AND TRAFFIC COPS | HEINRICH HEESCH | WOLFGANG HAKEN | ENTER THE COMPUTER | COLOURING HORSESHOES 10. Success! ... 190 A HEESCH -HAKEN PARTNERSHIP? | KENNETH APPEL | GETTING DOWN TO BUSINESS | THE FINAL ONSLAUGHT | A RACE AGAINST TIME | AFTERMATH 11. ... but is it a proof? 214 COOL REACTION | WHAT IS A PROOF TODAY? | MEANWHILE ... | ANEWPROOF | THE FUTURE ... Notes and references 229 Chronology of events 245 Glossary 249 Picture credits 255 Index 257

Promotional Information

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

About the Author

Robin Wilson is Head of the Pure Mathematics Department at the Open University and Fellow of Keble College, Oxford University. He is Gresham Professor of Geometry at Gresham College, London, and is a frequent visitor to Colorado College. He has written and edited about 25 books on topics ranging from graph theory via philately, to the Gilbert and Sullivan operas, to the history of mathematics.

Reviews

"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

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