Mathematical Works Printed in the Americas, 1554-1700, Bruce Stanley Burdick, 2009, 373 pp., illustrations, bibliography, hardback, $55, ISBN 978-0-8018-8823-6, Baltimore: Johns Hopkins Press, www.press.jhu.edu
In 1921, David Eugene Smith published three works: an article in the American Mathematical Monthly and a translation and facsimile of the Sumario Compendioso (1556). Smith claimed in his writings that the Sumario Compendioso was the first mathematics book published in the New World. It was a Spanish book published either in Mexico or Peru to serve the needs of the gold and silver trade by listing exchange rates, discussing the computation of taxes, and explaining the procedures of simple arithmetic and algebra. This information, namely, that the first mathematics book written in the Americas was Spanish, not English, came as a jolting shock to many readers. While, in retrospect, the Spanish organized presence in the Americas was known to precede that of the Northern Europeans, little thought had been given to their intellectual or scientific accomplishments in their new colonies. Yes, indeed, the first mathematics and scientific books published in the New World were Spanish. Bruce Burdick has affirmed this in his detailed, annotated bibliography. In fact, he has discovered two earlier publications, a logic book and a book containing examples from geometry (including figures), both from 1554. The Sumario Compendioso remains the earliest work on arithmetic or algebra from the Americas.
Searching the libraries of the world, Professor Burdick assembled information on 259 works reflecting an interest in mathematics and compiled in the Spanish and English colonies of the Western hemisphere before 1700. While some of these works are mathematical texts per se, most, such as almanacs and ephemerides, depend on mathematics for their conclusions. The Spanish contributions far outweigh those of their northern neighbors. In many cases, Burdick does more than merely list the reference: he describes it in detail and explains its mathematical implications. Much can be learned in reading his explanations. Several supportive indices supply further information. Selected illustrations enrich some entries.
Historians of mathematics and science who are particularly interested in early American developments will find this book a treasure. This is a wonderful research resource.
Frank J. Swetz, Professor Emeritus, The Pennsylvania State University