*The Secret Life of Numbers: 50 Easy Pieces on How Mathematicians Work and Think*. George G. Szpiro, 2006. . Joseph Henry Press, 500 Fifth Street, NW, Washington DC20001. ISBN 0-309-09658-8, hardback, $24.95, 190 pages, with index and bibliographic resources. Also available for download as PDF File from National Academies Press [$0.60/chapter]. http://nap.edu

This is a delightful collection of vignettes ranging from short biographies of current and historical mathematicians to articles on applied mathematics in fields ranging from economics to botany to geography. The chapters were originally published as columns in the Swiss newspaper *Neue Zürcher Zeitung*. The distance of a few years has not seriously limited accuracy, although the Poincaré conjecture is addressed in both the chapter on “Unsolved Conjectures” and that on “Solved Problems.”

These articles are written for the layperson, and as such, they provide a rich source of interesting overviews that a teacher could use to enliven mathematics lessons. They are also accessible to high school students, and would be useful as starting points for short reports. Such readings might motivate students both to see mathematicians as real people [and not all weird ones at that!] and to see uses of mathematics that respond to the perpetual “When are we ever going to use this?” query. Chapter 14(pp. 55-58) on Abel is an example of lovely exposition combining history and an elementary description of group theory. Inevitably, in short articles for the layperson there are some inaccuracies or unclear statements. Szpiro uses the word “proof” too loosely for a mathematician, as in accepting statistical analysis that “proves” authorship through data compression comparisons (p. 154).

Overall, I recommend this book highly as a pleasant read and a useful addition to educators’ libraries.

Edith Prentice Mendez, Associate Professor of Mathematics, Sonoma State University

See also the MAA Review by William J. Satzer.