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Four Colors Suffice

Frank J. Swetz, reviewer

Four Colors Suffice: How the Map Problem was Solved, 2002. 280 pp., illustrations, $24.95 cloth. ISBN 0-691-11533-8. Princeton University Press, 41 William Street, Princeton, NJ 08540 (800) 777-4726,

"Can every map be colored with at most four colors so that all adjacent countries are colored differently?" So is stated one of the most famous problems in modern mathematics. While this issue would seem a concern of cartographers, it was not. The conjecture was first proposed by Francis Guthrie, a British mathematician, in the middle of the nineteenth century. From that time until 1976, when the solution was resolved by Wolfgang Haken and Kenneth Appel, two American mathematicians using a computer, the problem gave rise to some fruitful mathematical theories and development. Robin Wilson, mathematician, Senior Lecturer at Britain’s Open University and historian of mathematics, in this delightful account, traces the history of this problem from its inception to its solution. The writing is concise, full of mathematical insights and enlivened with wit. Wilson takes the reader inside the thinking and arguments of the many mathematicians who tackled the problem, from the eccentric Percy John "Pussy" Heawood (1861-1955), to Harvard’s George David Birkhoff (1884-1944), to the Technical University of Hanover’s Heinrich Heesch (1906-95). The tale of this problem and its solution is certainly an example of international cooperation. Information supporting illustrations abounds.

This book is truly an example of excellent historical reporting in mathematics. Both for its content and style, Four Colors Suffice is highly recommended to anyone who has an interest in the history of mathematics. Teachers should note how one can tell a story, while still doing some very good mathematics.

Frank Swetz, Professor Emeritus, The Pennsylvania State University

See also the MAA Review by Gerald L. Alexanderson.

Frank J. Swetz, reviewer, "Four Colors Suffice," Convergence (September 2008)