Mathematics and The Historian’s Craft: The Kenneth O. May Lectures, G. Van Brummelen, M. Kinyon, ed, 2005, 357 pp., 91 illustrations, $89.95, hardcover, ISBN 0-387-25284-3, Springer-Verlag www.springer-ny.com.
Mathematics and The Historian’s Craft is a publication of the Canadian Mathematical Society. The lectures were given in honor of Kenneth O. May a beloved Canadian mathematician and historian who was instrumental in helping make the Canadian Society for History and Philosophy of Mathematics (CHSPM) the strong organization it is today. There are 12 lectures in the collection and there is something of interest included for anyone who either teaches mathematics or is interested in the historical development of the subject. Some of the articles are for the more historically minded but are well worth reading by anyone interested in mathematics. A consistent theme is that a lot of the mathematics we study now was developed in response to questions that have little to do with how the math is used today. As a teacher of upper level secondary mathematics, I found the following chapters particularly interesting and would recommend them to anyone in the secondary field:
"Mathematics, Instruments and Navigation (1600–1800)" by Jim Bennet - A fascinating study of how some of what we teach at the algebra 2-precalculus level resulted from solving navigation problems which surfaced as a result of the tremendous increase of trade related travel during that time.
"Was Newton’s Calculus a Dead End? The Contnental Influence of Maclaurin’s Treatise of Fluxions" by Judith Grabiner – A must read for anyone who teaches calculus – this contains lots of interesting insights into the Leibniz- Newton controversy about who really developed calculus.
"The Mathematics and Science of Leonhard Euler ( 1707 – 1783 )" A very readable introduction to Euler and his work which gives one a real sense of how important his work was both in his time and now.
"The Battle for Cantorian Set Theory" A good introduction to both Cantor’s work on the Infinite and the battle for its acceptance. This would be well worth reading by anyone who is introducing the concept of the infinite into a course.
Also worth reading were talks on Hilbert’s 24 Problems, Turing’s influence on the development of AI, and a very interesting piece on Mathematics and Gender. This is a book that has something for everybody and would be a great addition to a school or departmental library. If you are interested in the topics I have mentioned or in the history of mathematics and how it is presented I recommend Mathematics and The Historian’s Craft to you highly.
Jon Choate, Mathematics Department, Groton School, Groton, MA