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A Contextual History of Mathematics

Frank J. Swetz, reviewer

A Contextual History of Mathematics.  Ronald Calinger, 1999, 751 pp., $106.00, paper. ISBN 0-02-318285-7, Upper Saddle River, NJ:  Prentice Hall.

Several years ago, I was approached by a representative of a textbook publishing company who asked, “What books was I interested in writing?”  I responded that I was going to write “the calculus book”, building on my teaching experience, research evidence on mathematics learning, and the features of successful calculus books.  He said the idea was great but his company would not be interested – the book wouldn’t sell. Publishing companies desired broad based, utilitarian products that  appeal to large audiences, i.e. big markets.  Ron Calinger has written his “the history of mathematics book,” including all those features he and many of the mathematics history community would like to see in a book: cultural, political and economic contextual background, biographical sketches and anecdotes, bibliographic information, current research theories and, of course, a detailed accounting of the development of mathematics itself. It seems like all those marginal notes he collected over the years ended up in this book.  The result of this effort will provide a fascinating read for a few individuals but, I’m afraid, also a frustrating experience for many.

The book is information dense, a cornucopia of facts with a welter of names, dates and events.  A less sophisticated reader can soon become lost.  For example, al-Khwarizmi’s name and works are introduced before the reader learns his identity.  In the sections on “Islamic Mathematics,” we come across the terms falsafa (p. 342) and Faylasufa (p. 344), but are never told what they mean.  We learn that Pascal communicated with “Roannez” (p. 534).  Who is he?  In following the labyrinth of political intrigues during the “Age of Absolutism” we come across cameralist doctrines (p. 560).  What is a cameralist?  Certainly, context is important in the history of mathematics – what events and conditions shaped and constrained the development of mathematics are very basic to its understanding.  However, context must be carefully directed and for the naïve reader, unfortunately, sometimes explained.  A judicious inclusion of time-lines and charts would have helped in this task.

This is a scholarly work: well footnoted, amply illustrated and containing an excellent bibliography of “Suggested Further Reading.”  For instructional purposes, a website has been proposed to supply supporting materials: advice, syllabi, questions, etc.  However, its function appears limited to supplying images of 49 typewritten pages of suggested examples for Chapters 1 – 13.  In total, the book contains seventeen chapters spanning the growth of mathematics from the Stone Age to the early 18th century.  A Contextual History of Mathematics could be used for graduate seminars in mathematics history and provide a useful library resource.

Frank J. Swetz, Professor Emeritus, The Pennsylvania State University

See also the MAA Review by Eisso Atzema.

Frank J. Swetz, reviewer, " A Contextual History of Mathematics," Convergence (July 2007)