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The measure of our intellectual capacity is the capacity to feel less and less satisfied with our answers to better and better problems.
In J.E. Littlewood A Mathematician's Miscellany. Methuen and Co., Ltd. 1953.
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Review of The Math Book
The Math Book: From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics, Clifford A. Pickover, 2009. 528 pp. illustrations, bibliography, index. $29.95 hardcover, ISBN: 978-1-4027-5796-9. Sterling Publishing Inc. 387 Park Ave. S., New York, NY 10016–8810. Phone: 212–532–7160, www.sterlingpublishing.com
I have often said that a good book is not merely written or compiled; it is crafted. That is, the book is designed for a specific audience and the textual and sensory format is carefully chosen for that audience. Clifford Pickover’s latest venture into the history of mathematics is such an endeavor. This is a wonderful book that presents an eclectic selection of mathematical concepts, personalities, and events that are chronologically organized from 150 million BCE to the year 2007. The author admits that this is a personal selection of happenings that stirred his curiosity. Still, I found this collection fascinating and most informative. Individual narratives are limited to one page and accompanied by a beautiful and often intriguing color illustration. Many of the illustrations are computer-generated. Indeed the illustrations are of such excellent quality and composition that they themselves provide a tour de force of mathematical ideas.
Even a very knowledgeable student of the history of mathematics will find much new information in this book. For example, I learned of James Alexander's (1888–1971) topological marvel, the horned sphere; Viggo Brun’s constant (1885–1978); and Emile Borel’s (1871–1956) normal numbers. Of course, many familiar topics such as the Golden Ratio, the abacus, and the tragic death of Hypatia are also included. Historically eminent mathematicians such as Pierre de Fermat (1601–1665), Giuseppe Peano (1858 –1932), Emmy Noether (1882–1935), and Kurt Gödel (1906–1978), along with many others, stare out at the reader from the illustrations. The entry for the year 1957 is about Martin Gardner (1914–2010). This is the year Gardner began his “Mathematical Games” column in Scientific American. The accompanying illustration (p. 409) shows Gardner standing before a bookshelf containing his many writings and is prefaced by the comment, “Martin Gardner stands by all his words.” This is a wonderful tribute to the man.
While the explanatory discussions are brief, they are sufficiently substantive to serve the subject in question and to pique further interest in the topic. While Pickover reaches out culturally to include such non-western contributions to mathematical progress as Al-Khwarizmi’s Algebra and al-Samawal’s The Dazzling, Chinese accomplishments remain ignored. At the very least, Jiuzang suanshu (Nine Chapters on the Mathematical Art, c. 100 BCE), possibly the most influential mathematics book of all time, could have been mentioned. Despite this oversight, The Math Book is an excellent, stimulating, and inspiring book, easily accessible for popular reading as well as scholarly perusal. The price is a true bargain for a work of this quality. The book is highly recommended for library and personal acquisition, and it also is a perfect gift for any young person interested in mathematics.
Swetz, Frank J., "Review of The Math Book," Loci (June 2010), DOI: 10.4169/loci003493