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The Universal History of Numbers: From Prehistory to the Invention of the Computer [Paperback]

Georges Ifrah , David Bellos , E. F. Harding , Sophie Wood , Ian Monk
4.3 out of 5 stars  See all reviews (18 customer reviews)


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Book Description

October 9, 2000 0471393401 978-0471393405 1st
"Georges Ifrah is the man. This book, quite simply, rules. . . . It is outstanding . . . a mind-boggling and enriching experience." –The Guardian (London) "Monumental. . . . a fascinating journey taking us through many different cultures."–The Times (London)"Ifrah’s book amazes and fascinates by the scope of its scholarship. It is nothing less than the history of the human race told through figures." –International Herald Tribune Now in paperback, here is Georges Ifrah’s landmark international bestseller–the first complete, universal study of the invention and evolution of numbers the world over. A riveting history of counting and calculating, from the time of the cave dwellers to the twentieth century, this fascinating volume brings numbers to thrilling life, explaining their development in human terms, the intriguing situations that made them necessary, and the brilliant achievements in human thought that they made possible. It takes us through the numbers story from Europe to China, via ancient Greece and Rome, Mesopotamia, Latin America, India, and the Arabic countries. Exploring the many ways civilizations developed and changed their mathematical systems, Ifrah imparts a unique insight into the nature of human thought–and into how our understanding of numbers and the ways they shape our lives have changed and grown over thousands of years. "Dazzling."–Kirkus Reviews "Sure to transfix readers."–PublishersWeekly


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 --This text refers to an out of print or unavailable edition of this title.

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. --This text refers to an out of print or unavailable edition of this title.

Product Details

  • Paperback: 656 pages
  • Publisher: John Wiley & Sons; 1st edition (October 9, 2000)
  • Language: English
  • ISBN-10: 0471393401
  • ISBN-13: 978-0471393405
  • Product Dimensions: 9 x 9.5 x 1.8 inches
  • Shipping Weight: 3 pounds
  • Average Customer Review: 4.3 out of 5 stars  See all reviews (18 customer reviews)
  • Amazon Best Sellers Rank: #1,796,833 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews
67 of 71 people found the following review helpful
5.0 out of 5 stars Quite simply the best book on numbers ever written March 8, 2000
Format:Hardcover
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.
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40 of 43 people found the following review helpful
5.0 out of 5 stars Extremely well researched book January 12, 2000
By A Customer
Format:Hardcover
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!
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25 of 28 people found the following review helpful
5.0 out of 5 stars Excellent work numbers April 26, 2000
Format:Hardcover
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.
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41 of 51 people found the following review helpful
2.0 out of 5 stars A deception? September 15, 2002
Format:Hardcover
This book is getting raves from intelligent readers who are not
experts in the history of numbers. But it sure isn't getting good reviews from experts. A group of scholars in France was disturbed by the uncritical popularity of the French edition,
and released a report calling the French edition "historically
unacceptable, a deception." [Bulletin de l'Association des
Professeurs de Mathematiques de l'Enseignement Publique 399 June 1995)] (I got this quote from Joseph Dauben's book review.)
More recently, in the January 2002 and February 2002 issues of
the Notices of the American Mathematical Society, Joseph Dauben
of Lehman College at CUNY critiqued the English tranlations of this book and its companion, "The Universal History of Computing." Professor Dauben consulted a number of experts in specialties such as the history of Arabic mathematics, Hindu mathematics, Mesopotamian mathematics, Chinese mathematics, and Mayan mathematics. His review is skeptical.
I'll quote various lines from Dauben's January review:
"...he[Ifrah]either wrote to the wrong experts, was indifferent to their responses, or was not prepared to settle for their inconclusive results and the tentative nature of their research."
"...Ifrah offers nothing but certainties." (when writing about
the Hindu-Arabic number system)
"[James]Ritter simply declares all of this to be false, due to an erroneous conflation of sources. First of all, he takes Ifrah's list to be a contrived amalgamation of names coming from
all epochs." (James Ritter is an Assyriologist at Universite de Paris VIII, the quote is about Ifrah's conclusions about Sumerian numbers.)
Read Professor Dauben's review. Afterwards, George Ifrah's fun-to-read, plausible book won't count for as much.
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11 of 13 people found the following review helpful
5.0 out of 5 stars 5000 years in the fascinating story of numbers May 3, 2002
Format:Paperback
One day, the young "devils" in a high school's mathematics class in France, asked some "plain" questions to their teacher: "When the numbers were invented?", "What is the history of the number Zero?", "How the ancients began writing down symbols for the numbers?" and so on... And these questions, changed the life of Georges Ifrah, the mathematics teacher in our story. He began his long voyage in the history of numbers and mathematics, through all mysterious ancient civilizations.
"Universal History of Numbers" is a huge, marvellous, fascinating story which deals with the birth of essential concepts in numbering systems in our distant past. Ifrah chases the clues in ancient sumerians hexagesymal system; the magical hieroglyphes of ancient Egyptians; the mysterious Maya and their counting system; Hebrew, Greek and Roman numbers with the mystics of "gematria"; sacred numerical signs of ancient Indus civilization and China, and much much more.
This is not just a "history of numbers"; Ifrah's work is a brilliant study on the roots of our civilization. While dealing with the numbers, he also presents us a perfect panorama of ancient cultures, such as the Maya calendar, the Vedic philosophy, Ancient Sumerian myths or the stories of Egyptian gods, in a very entertaining style. If you are interested with the roots of civilization and "ancient wisdom", you must read this excellent book - you'll never regret.
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Most Recent Customer Reviews
5.0 out of 5 stars A Phenomenal Piece of Work
This is by far the most comprehensive work on number that I have ever read.
I'll give my opinion of the book and then offer suggestions for other readers. Read more
Published 20 days ago by ArthurW
5.0 out of 5 stars Best History of the Numbers
This is the best history of the numbers that I have read,
and I have read quite a few. It is comprehensive and
detailed.
Published 1 month ago by Indikos
1.0 out of 5 stars Book condition not as described by seller
Had I known that the book has "Library" stamps all over it I would not have purchased it. I am now stuck with a book that I have to hide from friends and visitors because... Read more
Published 7 months ago by Jabber Wock
5.0 out of 5 stars Finding out about numbers.
My 6th grade students are loving this book. We are finding out the who, what, where, and why of everything mathmatical.
Published 10 months ago by Amazon Customer
5.0 out of 5 stars An exhaustive book on history of numbers
This book is an enjoyable as well as an encyclopedic work, referencing an immense amount of historical material in great detail.

I have read Dauben's critical review. Read more
Published on July 15, 2011 by Sinha
3.0 out of 5 stars good book
My husband was so pleased with this book,in very good condition and lots of learning to be had.
Published on June 24, 2010 by faye
5.0 out of 5 stars Simply A Must Read!
This is simply a must read for anyone who is interested in numerical literacy!

Indispensable and should be required curriculum for anyone who teaches who wishes to think... Read more
Published on July 19, 2009 by D. GREEN
4.0 out of 5 stars From a history point of view , very good
As someone who deals a lot in the theory of numbers,
the book seems somewhat useless in modern algorithmic terms,
but in terms of the history of how numbers were thought... Read more
Published on December 11, 2008 by Roger Bagula
5.0 out of 5 stars The Universal History of Numbers: From Prehistory to the Invention of...
I believe for many amateurs interested in the history of numbers, this is the only book they ever need. Amazingly thorough! Read more
Published on November 13, 2007 by Eric Zhang
5.0 out of 5 stars math history you can use
I am a teacher and I love this book. I use it to teach counting systems to young children. I like having access to all kinds of math of the past. Read more
Published on August 7, 2007 by Alice Cotton-royer
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