The Universal History of Numbers: From Prehistory to the Invention of the Computer (Hardcover)

by Georges Ifrah (Author) "There must have been a time when nobody knew how to count..." (more)
Key Phrases: written numeral systems, corresponding numerical symbols, alphabetical numeration, Mount Meru, Middle Ages, North Africa (more...)

Editorial Reviews

Amazon.com Review
The title doesn't lie. Mathematician Georges Ifrah's masterpiece, The Universal History of Numbers, is a wonderfully comprehensive overview of numbers and counting spanning all the inhabited continents as far back in time as records will allow us to look. Beyond the ancient Babylonians, Sumerians, and Indians, Ifrah takes us farther south into Africa to examine an early decimal counting system and into ancient Mexico to reconstruct what we can of the Mayan calendar and numerical system. The 27 chapters are chiefly organized by culture, though there are some cross-cultural overviews of topics like letters and numbers.

The author's aim was grand: "to provide in simple and accessible terms the full and complete answer to all and any questions ... about the history of numbers and counting, from prehistory to the age of computers." This led him to wander the world for 10 years, studying and learning; this scholastic pilgrim has returned with amazing stories to tell. Toward the end of the book, Ifrah makes the book truly universal by refuting alien-intervention theories of cultural origins--surely our benefactors would have given us an efficient decimal counting system, zero and all, before helping us build pyramids and such. Such charming ideas, combined with such rigorously researched facts, make The Universal History of Numbers a uniquely important and fascinating volume. --Rob Lightner

From Kirkus Reviews
Ifrahs monumental follow-up to From One to Zero (1993) goes from one to (almost) infinity as he meticulously reviews the numbers and reckoning systems of countless tribes and cultures in a dazzling scholarly performance. ``Performance'' is the operative word here, for not only does Ifrah enumerate the words and symbols used for arithmetic, but he also explains how to use each system, providing illustrations, diagrams, riddles, and puzzles. Indeed, nearly every page displays handsome numerals, counting devices, and illustrations of their use. Ifrah takes the human body as the aboriginal point of reference for most counting systemsfingers and toes producing systems using 5, 10, or 20 as a base. But 12, 60, and 360 have also been used, usually by cultures that attached more importance to the sky than to their anatomy. Ifrah gives special credit to the Mayans for their extraordinary adeptness at astronomical measurements, which calculated the length of the solar year as 365.242 days and the month at 29.53086 days. He commends India for the invention of zerothe placeholder in counting systems that use positional notation to indicate the different values, for instance, of 1, 10, and 100. A recurring theme is the intimate relation between number systems and written language. Just as the invention of alphabets allows the generation of myriad words, advanced number systems can use a limited number of symbols to represent any large number. A quibble or two: Ifrah frequently asserts that our brains cannot instantly number a collection of more than four objects, though psychologists maintain we can recognize up to seven objects without counting. And since many statements on the origins of systems and borrowings across cultures are speculative, they are subject to change in light of recent discoveries. A must for any libraryand a wonderful gift for anthropologists, ethnographers, cultural historians, and quiz kids. (Over 150 b&w drawings) (Book-of-the-Month Club selection; History Book Club selection; Quality Paperback Book Club selection) -- Copyright ©1999, Kirkus Associates, LP. All rights reserved.

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Product Details

• Hardcover: 656 pages
• Publisher: Wiley (November 19, 1999)
• Language: English
• ISBN-10: 0471375683
• ISBN-13: 978-0471375685
• Product Dimensions: 9.8 x 9.3 x 2 inches
• Shipping Weight: 3.6 pounds
• Average Customer Review: 4.4 out of 5 stars See all reviews (11 customer reviews)
• Amazon.com Sales Rank: #475,366 in Books (See Bestsellers in Books)

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Customer Reviews

Most Helpful Customer Reviews

58 of 61 people found the following review helpful:

5.0 out of 5 stars Quite simply the best book on numbers ever written, March 8, 2000

By	Mark Rosa (Anjiki Nakamachi, Japan) - See all my reviews (REAL NAME)

The scope of this book is simply unbelievable. Everything you've ever seen about numbers, plus everything you ever wanted to know, and then numbering systems you never even knew existed. Nothing short of fantastic.

A major expansion of Ifrah's earlier work, From One to Zero, the tone is a bit more scholarly than Lowell Bair's (the original translator's) relaxed style in the 1981 original, which makes you feel like you're having a chat with your professor. I really got the impression that Ifrah wanted a more serious work this time; something that could be consulted by experts. I'm not panning the book for this; it just makes for different reading. Plus, the addition of an index certainly makes the book easier to use for research.

Another nice addition was the increased use of typography for non-European text. While Ifrah's effort in hand-drawing everything in the 1981 version was admirable, it feels a bit strange reading handwritten characters in languages he doesn't know (Chinese, for example). Real fonts (like the ones used for Arabic) were a wise investment.

The section on gematria (using the numerical values of letters for divination, wordplay, etc.) is another reason to pick this book up. It seems that if people try hard enough, they can make just about anything into '666'. ^_^; He also went into detail about how different cultures actually did (and do) arithmetic -- mighty interesting stuff for math students and teachers even today!

In short, this is the world's definitive work on numerals. You simply won't find anything better, anywhere.

Also highly recommended: Number Words and Number Symbols by Karl Menninger, published by Dover Books.

38 of 40 people found the following review helpful:

5.0 out of 5 stars Extremely well researched book, January 13, 2000

By A Customer

In reading texts on history of numbers, one often finds books that suffer from partial viewpoints colored by cultural ignorances and biases. None of that here. One thing this book can't be accused of is superficiality. This book is simply awesome in its breadth and depth. Ifrah has successfully taken each culture's contribution to numbers and presented it with amazing clarity and perspective.

This version has many more improvements from its earlier incarnation titled From one to Zerowhich was a very remarkable book too.

Also a very good and natural introduction to doing math in number systems with different bases!

21 of 23 people found the following review helpful:

5.0 out of 5 stars Excellent work numbers, April 26, 2000

By	Sanjeev manohar (USA) - See all my reviews

Simply the best book on numbers I've read. Many other books on numbers are replete with inaccuracies and exaggerations based on cultural and educational biases. Not here. Ifrah's chapter on the India's contribution to numbers and how the Sanskrit language was used to communicate numbers is simply spectacular. A must read for anyone interested in mathematics.