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A Concise History of Mathematics. 4th ed. Dirk J. Struik , 1987, vii + 228 pp.+ ill. .$ 9.95 paper. ISBN 0486602559. New York: Dover Publications, http://store.doverpublications.com

Among the enduring books on the history of mathematics written in English is that by Dirk J. Struik (1894 – 2000). A gifted mathematician, his interest in its history began early in his career. Having earned the Ph.D. in Mathematics at the University of Leiden in 1922, he focused on tensor calculus until the mid 1930s when its central importance waned. During this later time Struik turned to a nascent interest, the history of mathematics, the field that soon occupied all his attention. The first major fruit of this study was *A Concise History of Mathematics*, published in 1948 in two volumes and continuous pagination (definitely pocket size). Struik saw it through three single volume revised editions, 1948 (sic), 1967, and 1987, with translations into Chinese (1956), Ukrainian (1961), German (1961), Russian (1964), and his own into Dutch (1965).

Within just 228 pages the account of the history of mathematics is adequately described as Concise. What then did he have in mind when he wrote? He wished to introduce his readers to the history, stir their interest, and then supply resources through which they could pick and choose for further study. Following his brief “Introduction” are eight pages of references beginning with the rubric “English texts to be consulted are” that include all the major reference works, both texts and periodicals, in English, French, German, and Italian. Each of the eleven chapters also contains has its own bibliography.

The underlying bond that ties the work together is Struik’s conviction on the social origins of all mathematics. “He belonged to the school of historians of mathematics that believed ‘that theorems are produced in a social context, and understanding the context is part of understanding how they arise’” (A Memorial by Chandler Davis, who knew DS personally; see Notices of the AMS, June/July 2001, vol. 48, pp. 584 ff). Or as Struik wrote in resume, “. . . we have been able to give a fairly honest description of the main trends in the development of mathematics throughout the ages and of the social and cultural setting in which it took place” (Concise History, p. 1). The first section of each chapter offers an overview of the socio-historical environment in which mathematics germinated and grew. For instance, “”Counting by fingers, that is, counting by fives and tens, came only at a certain stage of social development. Once it was reached, numbers could be expressed with reference to a base . . .”(p. 11). As the reader soon discovers, the social environment requires attention to the persons who developed the mathematics to fit not only its own needs but also the needs of society. Pierre-Simon Laplace, “the last of the leading eighteenth-century mathematicians, . . . easily shifted his political allegiances” from King, to Republic, to Emperor, and back to the King “to continue his mathematical activity despite all political changes in France” (p. 135).

Quite deliberately, Struik left out many influential mathematicians. For this he apologized: “. . . many relatively important authors—Roberval, Lambert, Schwarz—had to be bypassed” for the sake of “a book of about two hundred pages” (CH, p. i). He wanted a book that people could read through in a short time without being bogged down by seemingly endless, however interesting, details whether mathematical or personal. Perhaps no other chapter shows Struik’s command of the field than the last, “The First Half of the Twentieth Century.” Here you discover the phenomenal growth of mathematics: who did what with whom, why and where (in Europe and the United States) up to the birth of the Computer Era.

*A Concise History of Mathematics* is an amazing book to read. What a tremendous amount of information Dirk Struik had at his command!

Barnabas Hughes, O.F.M., Professor Emeritus, California State University, Northridge

Barnabas Hughes, reviewer, "A Concise History of Mathematics," *Convergence* (July 2007)