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[About Fourier:] It was, no doubt, partially because of his very disregard for rigor that he was able to take conceptual steps which were inherently impossible to men of more critical genius.
In P. Davis and R. Hersh, The Mathematical Experience, Boston: Birkhauser, 1981.
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Pascal's Arithmetical Triangle
Pascal's Arithmetical Triangle: The Story of a Mathematical Idea, A. W. F. Edwards, 2002, 202 pp., illustrations, $18.95 paperback. ISBN 0-8018-6946-3. The Johns Hopkins University Press, 2715 N. Charles Street, Baltimore, MD 21218-4319, www.press.jhu.edu.
In recent years numerous surveys of broad mathematical topics - suitable for the general reader who has more than a passing interest in mathematics and its history - have appeared on the scene. Because such treatments tend to be quite historical in nature, this reviewer has often found them to be useful classroom tools in teaching courses in the history of mathematics. He has, for example, successfully used P. Nahin's An Imaginary Tale, J. Arndt and C. Haenel's Pi Unleashed, and H. Walser's The Golden Section as basic source material for student presentations in such a course. Pascal's Arithmetical Triangle compares quite favorably with the aforementioned books and others in this milieu as offering a dependable, accessible resource for college mathematics majors to use in learning about specific historical topics. Professor Edwards has carefully researched and tightly organized his historical/mathematical account of Pascal’s triangle. However, because many of its mathematical ideas and notations are advanced in nature, only a gifted, interested high school student would be able to engage this account successfully. On the other hand, in addition to undergraduate history of mathematics students, most college students in discrete mathematics or combinatorics courses should be able to read this book and learn much about the history and mathematical applications of Pascal’s Triangle. Finally, all four books noted above have been reviewed for MAA Online @ www.maa.org. In particular, Professor Herbert Kasube gives a very positive (and more extensive) review of Edwards' book on this website.
Richard M. Davitt, Professor of Mathematics and Distinguished Honors Fellow, University of Louisville