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The Philosophical Implications of the Four-Color Problem

by Edward R. Swart

Year of Award: 1981

Award: Lester R. Ford

Publication Information: The American Mathematical Monthly, vol. 87, 1980, pp. 697-707

Summary: In response to criticism of the computer-dependent proof (as a posteori justification) of the four-color problem, this article argues that it is reasonable to regard all mathematical truths as a priori, no matter how they are arrived at.  In doing this the author introduces a new mathematical entity intermediate between a conjecture and a theorem.

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About the Author: (from The American Mathematical Monthly, vol. 87 (1980)) Edward R. Swart received a D.Sc. from the University of Pretoria in 1957 and a Ph.D. from the University of Witwatersrand under D.S. Henderson in 1977. He was formerly at the University of Rhodesia, where he was Director of the Gulbenkian Centre 1966-77, Dean of the Faculty of Science 1973-75, Professor and Head of the Department of Computer Science 1975-77. He is also past President of the Rhodesia Scientific Association 1973-74. He is now a Professor in the Department of Combinatorics and Optimization at the University of Waterloo. His main research interest is in graph-theoretic problems concerned with colorings and flows. He was one of the five authors cited by Haken and Appel in their initial announcement of the proof of the four-color theorem.


Subject classification(s): Discrete Mathematics | Graph Theory | Index | Mathematics History | Famous Problems
Publication Date: 
Wednesday, September 24, 2008