Title: Wonders of Numbers: Adventures in Mathematics, Mind and Meaning
Author/Artist: Clifford A. Pickover
Publisher: Oxford University Press
Reviewer: Paul Taylor
The industrious Pickover has produced a compendium of mathematical ideas presented through a series of puzzles that lead the reader to further explorations. To many people, mathematics will seem a forbidding subject, inaccessible to all but the expert, but the first chapter is very pleasingly devoted to the amateur:
Are you a mathematical amateur? Do not fret. Many amazing mathematical findings have been made by amateurs, from homemakers to lawyers. These amateurs developed new ways to look at problems that stumped the experts.
Here is one of the examples:
In the 1970s, Marjorie Rice, a San Diego housewife and mother of five, was working at her kitchen table when she discovered numerous new geometrical patterns that professors had thought were impossible. Rice had no training beyond high school, but by 1976 she had discovered 58 special kinds of pentagonal tiles, most of them previously unknown.
The puzzles are set by a merciless character called Dr Googol in the course of 125 well-illustrated chapters ranging over all kinds of mathematics, from Mozart Numbers to Everything You Wanted to Know About Triangles But Were Afraid to Ask.
As an interlude from the puzzles, the second part of the book includes surveys and lists, such as A Ranking of the 10 Most Interesting Numbers, and The Unabomber's Ten Most Mathematical Technical Papers.
This is an extremely stimulating book that will challenge most readers and might be a good way of interesting young people in the fascinating and hugely important subject of mathematics.
Oxford University Press provides a web site containing computer program listings for the problems in the book: http://www.oup-usa.org/sc/0195133420/, and Clifford Pickover's home page is at http://www.pickover.com/
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