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The mathematician is entirely free, within the limits of his imagination, to construct what worlds he pleases. What he is to imagine is a matter for his own caprice; he is not thereby discovering the fundamental principles of the universe nor becoming acquainted with the ideas of God. If he can find, in experience, sets of entities which obey the same logical scheme as his mathematical entities, then he has applied his mathematics to the external world; he has created a branch of science.
Aspects of Science, 1925.
Loci: Convergence
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Mathematical Works Printed in the Americas, 1554-1700
Mathematical Works Printed in the Americas, 1554 -- 1700, Bruce Stanley Burdick, 2009, 373 pp., illustrations, bibliography, hardback, $55, I SBN - 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 Mathematics Monthly; and a translation and a facsimile concerning the Sumario Compendioso (1556). As Smith revealed in his writings, the 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 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 proceed 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.
Searching the libraries of the world, Professor Budick 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 this 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