*How Mathematics Happened: The First 50,000 Years*, by Peter S. Rudman, 2007, 461+xiii pp. Hardcover, $26.00, ISBN 978-1-59102-477-4, Prometheus Books, 59 John Glenn Drive, Amherst, New York 14228-2197 www.prometheusbooks.com

"As far as most people know or care, our number system and the arithmetic we do with it descended from Mount Sinai inscribed on the reverse side of the Ten Commandments: 'Thou shalt count with the decimal system using the ten symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9; and do arithmetic thus and so.' " The opening sentence of this informative, entertaining chronicle of the early history of mathematics, illustrates the casual writing style of a text that provides easy to understand information for a general audience. Archaeological evidence for our current knowledge is carefully explained. Rudman succeeds in explaining the mathematics of ancient civilizations in a way that enables the serious, but not necessarily mathematically trained reader, to gain a thorough understanding of the concepts. For example, rather than providing a sophisticated mathematical presentation of the process of Egyptian division, the author talks about how a child, in ancient Egypt or the modern day world, might solve the problem of eight children equally sharing seven melons. For the interested reader, fun questions are presented throughout the book to test comprehension; the appendix supplies answers. Rudman does a superb job illustrating the nature of geometric algebra used by the Babylonians. Teachers of algebra will find the diagrams a wonderful tool for helping students in their classrooms "see" how particular formulas are often easily justified by pictures. The final chapter, "We Learn History to be Able to Repeat It," provides Rudman's views on the appropriate way to teach mathematics in our current classrooms. His basic premise is that we need to make mathematics interesting and using history is a valuable tool for that goal.

I recommend this book for those interested in ancient mathematical history and desirous of an easy read. It is also an excellent resource for mathematics teachers who wish to enrich their students' knowledge of and appreciation for the historical roots of the mathematics used today.

Gail Kaplan, Associate Professor, Towson University, MD

See also the MAA Review by Amy Shell-Gellasch.