In THE BOOK OF NUMBERS, two famous mathematicians fascinated by beautiful and intriguing number patterns share their insights and discoveries with each other and with readers. John Conway is the showman, master of mathematical games and flamboyant presentations; Richard Guy is the encyclopedist, always on top of problems waiting to be solved. Together they show us why patterns and properties of numbers have captivated mathematicians and non-mathematicians alike for centuries. THE BOOK OF NUMBERS features Conway and Guy's favorite stories about all the kinds of numbers any of us is likely to encounter, and many others besides. "Our aim," the authors write, "is to bring to the inquisitive reader. . .an explanation of the many ways the word 'number' is used." They explore patterns that emerge in arithmetic, algebra, and geometry, describe these pattern' relevance both inside and outside mathematics, and introduce the strange worlds of complex, transcendental, and surreal numbers. This unique book brings together facts, pictures and stories about numbers in a way that no one but an extraordinarily talented pair of mathematician/writers could do.
The authors are well known to both academic and recreational mathematicians-Conway for inventing the "game of life" and discovering surreal numbers and Guy as the editor of the "Unsolved Problems" section in American Mathematical Monthly. They also coauthored the classic Winning Ways for Your Mathematical Plays (Academic, 1982). This popularization of number theory looks like another classic. Though number theory does not lend itself to fun and games, the authors take such joy in the order and patterns of numbers that you can't help being fascinated by what is actually a fairly difficult subject. A combination of clear verbal explanations, wonderfully clever diagrams, and equations (for the real mathematicians) make sometimes complicated numerical concepts accessible to those "without particular mathematical background" (i.e., who are not at least graduate students in mathematics). The material is simplified but not dumbed down. A bridge to understanding and appreciating higher mathematical concepts, this book could appeal to anyone from a mathematically sophisticated high school student to a university mathematics professor.-Amy Brunvand, Univ. of Utah Lib., Salt Lake City