History of Mathematics

A History of Mathematics, Second Edition, Carl B. Boyer, Revised by Uta C. Merzbach, March 1991, 736 pp. $39.95 soft.  ISBN 0471543977. New York: John Wiley & Sons, Inc., http://www.wiley.com

One can enhance the reward of teaching the history of mathematics by choosing a good text. Some students appear quite comfortable struggling through tersely presented material while others respond favorably to simple lecture augmented by selected readings.  Educators can readily address the needs and varied capabilities of their audience by choosing this second edition of A History of Mathematics, by Carl B. Boyer, as its conversational tone engages both the novice and the veteran mathematician immediately. 

The text begins its comprehensive historical journey with a discussion about the origins of numbers, as well as the mathematics of the ancient Egyptians, Mesopotamians and Greeks.  By the end of the text, the reader has investigated mathematical discoveries up to the twentieth century.  Thoughtfully included in the appendix is a chronological table that gives the reader quick access to a timeline detailing changes in the ruling power structure, milestones of modernity, and of course the appearance of important mathematical publications.  An expansive bibliography is detailed for each chapter for those interested in learning more on any one topic.

Carl Boyer’s History first appeared in 1968. He died in 1976 and the revision and updating was carried out by Uta Merzbach, former Historian of Mathematics at the Smithsonian Institution. This version of Boyer intentionally targets readers outside the classroom as it deliberately omits the exercises found at the end of each chapter in earlier editions.  This dampened some of my inherent curiosity, given that I like to explore these types of problems.  I found that I wanted exercises to do, and, at a minimum, I would have liked to have seen what Boyer found to be interesting enough to question or investigate further.

Boyer’s History wonderfully summarizes notable achievements in mathematics; however not all geographic regions get equal billing. For example Boyer condenses Arabic contributions to one chapter, and the mathematical developments from China and India share one chapter. Meanwhile, discussion of work done by the ancient Greeks and Europeans from medieval times through the 19th century dominate the rest of the twenty-eight chapter text.   Also noticeably lacking is the presence of women and their contributions to mathematical society.  For example, Boyer credits Hypatia for writing commentary on the works of Diophantus, Ptolemy and Apollonius, however no exploration of the commentary follows.  In two separate sentences, Sonya Kovelevskaya’s career is unduly shortened to only noting her extension of the work of Cauchy and her role as a protégé of Mittag-Leffler.   If an educator were to choose History as the primary text for a history of mathematics course, this lack of balance would need to be addressed with supplementary lecture notes to meet the needs of today’s increasingly diverse classroom.

Despite these imbalances, I still found Boyer’s History likeable, easy to read, and full of good reference material.  Ultimately it is the mathematics, and not political correctness, that grabs and keeps the reader’s attention.  I would certainly recommend adding a copy of Boyer’s History to your history of mathematics resource library.

Kathleen Ambruso Acker, Mathematics Dept., Cabrini College, Radnor,PA

See also the MAA Review by Jason M. Graham.