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Math through the Ages

Victor J. Katz, reviewer

Math through the Ages: A Gentle History for Teachers and Others , by William P. Berlinghoff and Fernando Q. Gouvêa. Oxton House, 2002. Paperback, 224pp., $19.95. ISBN 1-881929-21-3.


Where does pi come from? Why should we be interested in negative numbers, or square roots of negative numbers? How did people ever figure out the quadratic formula? The answers to these and many other similar questions asked by college and secondary teachers and their students can be found, in easily accessible form, in this wonderful little book by two faculty members at Colby College.

Although knowledge of the history of mathematics is an important tool for mathematics teachers at the secondary and college level, it is not always simple to find out about the history of a particular topic. There are many solid texts in the field, but often the history of the quadratic equation, for example, is spread among several chapters because it extends through many cultures and many centuries. In this book, on the other hand, the basic story can be found immediately by turning to chapter 10.

The authors call this book "a gentle history," and indeed it is. It very carefully gives the reader capsule histories of such topics as zero, symbols in algebra, solving cubic equations, the Pythagorean theorem, sines and cosines, and elementary statistics, among many others. Each short chapter discusses the history of a particular idea, often spanning centuries and civilizations, but always clearly and concisely. It is written so that a teacher can dip in wherever she wants, find the information she needs, and use the information in classes or answer questions of her students.

But if the teacher wants more than these capsule histories, the first section of the book, entitled "The History of Mathematics in a Large Nutshell," will help. Here, the authors treat the history of mathematics chronologically, from its beginnings in ancient Egypt and Mesopotamia up to the development of computers in the late twentieth century. This section thus provides a broad overview that will help the reader place the individual chapters in context.

And if the reader wants to go deeper into any particular subject, or into the history of mathematics as a whole, the authors again provide guidance, first with a suggested reference shelf of books to which to turn to find more information, then with a list of "fifteen historical books you ought to read" (in their entirety), and finally with a brief tour of historical sources on the Internet. Finally, the book contains a marvelous bibliography of other works referred to in the various chapters.

Math through the Ages is a very well-organized and thus a very user-friendly book. It will be a wonderful resource for teachers at all levels. And since it sells for a very reasonable price, it should be part of every teacher's personal library.


Victor J. Katz, University of the District of Columbia

Victor J. Katz, reviewer, "Math through the Ages," Convergence (July 2007)