The Mystery of Numbers, Marc-Alain Quaknin, 2004, 383pp. $24.95, cloth, bibliography, illustrations, ISBN 284323 6300. New York: Assouline Publishing, 212-989-6810,http://www.assouline.com/.
This book takes the reader on a journey through numbers, from the earliest beginnings in India to the contemporary searches for perfect numbers and Wiles' proof of Fermat's Last Theorem (1993). Although the book in its discussions references a good number of mathematicians, the mention is only in passing. Make no mistake; this book focuses on numbers and not mathematicians, and Quaknin provides a detailed review of how our present system of numerals came to be and how it traveled from Asia to Europe.
The book is roughly organized along three themes: numerals, numbers, and shape. These are only general categories, and do not really describe what follows. Shapes, for example, is not an investigation into geometry but rather a detailed discussion of magic squares, from their earliest existence in China to their modern representations. Quaknin also describes the Kabbalah in fine detail without becoming too pedantic.
This book could serve as a resource for either teachers or students. The mathematics displayed is clearly explained and supported by helpful visuals. It is useful to anyone who has a reasonable knowledge of algebra and geometry. Each chapter is brief (sometimes too brief) with sources that the reader can consult for more detail. The book contains many photographs of interesting artifacts from the history of mathematics, for example: the Plimpton tablet; the page of Liber Abaci that contains the famous Rabbit Problem and an illustration of the oldest manuscript page to display Hindu-Arabic numerals.
Art Johnson, Assistant Professor, Boston University