Number: From Ahmes to Cantor [Hardcover]

Midhat Gazale (Author)

Book Description

Publication Date: 2000

We might take numbers and counting for granted, but we shouldn't. Our number literacy rests upon centuries of human effort, punctuated here and there by strokes of genius. In his successor and companion volume to Gnomon: From Pharaohs to Fractals, Midhat Gazale takes us on a journey from the ancient worlds of the Egyptians, the Mesopotamians, the Mayas, the Greeks, the Hindus, up to the Arab invasion of Europe and the Renaissance. Our guide introduces us to some of the most fascinating and ingenious characters in mathematical history, from Ahmes the Egyptian scribe (whose efforts helped preserve some of the mathematical secrets of the architects of the pyramids) through the modern era of Georg Cantor (the great nineteenth-century inventor of transfinite numbers). As he deftly blends together history, mathematics, and even some computer science in his characteristically compelling style, we discover the fundamental notions underlying the acquisition and recording of "number," and what "number" truly means. Gazale tackles questions that will stimulate math enthusiasts in a highly accessible and inviting manner. What is a natural number? Are the decimal and binary systems the only legitimate ones? Did the Pythagorean theorem and the discovery of the unspeakable irrationals cost the unfortunate mathematician Hippasus his life? What was the Ladder of Theodorus of Cyrene and how did the ancient Greeks calculate square roots with such extraordinary proficiency? An original generalization of Euler's theorem is offered that explains the pattern of rational number representations. Later on, the field of Continued Fractions paves the way for another original contribution by Gazale, that of cleavages, which sheds light on the mysterious nature of irrational numbers as it beautifully illustrates Dedekind's famous Schnitt. In the end the author introduces us to the Hilbert Hotel with its infinite number of rooms, guests, and an infinite number of people waiting to check in, where he sets the debate between Aristotle and Cantor about the true nature of infinity. This abundantly illustrated book, remarkable for its coherency and simplicity, will fascinate all those who have an interest in the world of numbers. Number will be indispensable for all those who enjoy mathematical recreations and puzzles, and for those who delight in numeracy.

Editorial Reviews

Review

Payoff for a close read is more than the science of number -- [it is] the thrill of the subject. -- Choice

About the Author

Midhat Gazale is an international telecommunications and space consultant and Visiting Professor of Telecommunications and Computer Management at the University of Paris IX. He has served as President of AT&T-France, as Chairman of the Board for Sperry-France and for International Computers-France, and as an executive and research scientist for other major companies. He was made Chevalier dans l'Ordre National du Merite in 1981.

Product Details

• Hardcover: 297 pages
• Publisher: Princeton University Press (2000)
• Language: English
• ISBN-10: 069100515X
• ISBN-13: 978-0691005157
• Product Dimensions: 9.5 x 6.4 x 1.1 inches
• Shipping Weight: 1.4 pounds
• Average Customer Review: 5.0 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #381,821 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

10 of 10 people found the following review helpful:

5.0 out of 5 stars A superbly written and presented history of mathematics., July 3, 2000

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Midwest Book Review (Oregon, WI USA) - See all my reviews

This review is from: Number: From Ahmes to Cantor (Hardcover)

In Number: From Ahmes To Cantor, Midhat Gazale takes the reader on an historical survey of the concept of numbers ranging from the antiquarian civilizations of Egypt, Mesopotamia, Maya, Greek, and Hindi, to the Arab invasion of Europe and the Renaissance era. We are introduced to the fascinating and ingenious men of mathematical history, from Ahmes the Egyptian scribe whose efforts helped preserve some of the mathematical secrets of the architects of the pyramids, through the modern era of Georg Cantor, the great 19th Century inventor of transfinite numbers. Number: From Ahmes To Cantor is a superbly written combination of history, mathematics, and a little computer science as it relates to the history, acquisitions, invention, and meaning of numbers. Number: From Ahmes To Cantor is highly recommended reading for students of mathematics, and is an invaluable history completely accessible to the non- specialist general reader with an interest in the history of mathematics.

9 of 9 people found the following review helpful:

5.0 out of 5 stars Required Reading for Math Students, November 8, 2000

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"deeodell1" (Darien, CT USA) - See all my reviews

This review is from: Number: From Ahmes to Cantor (Hardcover)

This book provides a clear exposition of the history of numbers. I wish I had read this book during my college days. I found it invaluable in understanding rational, irrational, transcendental numbers, etc. Mr. Gazale has offered an original definition of real numbers. His generalization of Euler's Theorem is novel and powerful, yet so simple. This book should be a basis for math courses at colleges and universities nationwide.