Customer Reviews

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

5 star:		(9)
4 star:		(2)
3 star:		(2)
2 star:		(1)
1 star:		(0)

 

 

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.

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!

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.

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.

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.

I was intrigued enough by Mr. Peterson's review here to look at the review by Dauben that he mentions. My conclusion is that the Dauben review should be treated with a grain of salt. It's not particularly balanced. In some of the criticism of Ifrah from people with more degrees than he has, one gets just a whiff of jealousy that the reviewers didn't have the endurance to write the book themselves.

If they had, I doubt they would have done any better of a job. Ifrah's book isn't perfect, but one can't expect such a book to be. This book is huge, folks. Ifrah is only one human being who tried to synthesize dozens of fields in none of which he could expect to become an expert. I think he did his best and I find his writing style companionable. Of course he makes errors, but he says a lot more things very well. We should be mindful of the book's limitations. But we also have to be grateful for what Ifrah managed to do.

This book is subtitled "from Prehistory to the invention of the computer", which is a little misleading. The text really ends about the stage of Europe's adoption of "Arabic numerals".
This reader thought there were three main trends within the book.
1st. A history of how every culture formed its counting system, from Polynesians islanders, to Tierra del Fuego, various African tribes to ancient and extinct cultures, cuneiform, hieroglyphics, knot tying, tally sticks to body counting. The author's blurb says the author Georges Ifrah spent 10 years in a worldwide quest recording different culture's counting systems. The author is a truly unique man, nothing escapes this author.
2nd The overall views are interesting, and the illustrations are suburb. The different systems explained from a historical perspective are though provoking. The author does a wonderful job explaining how each system works.
3rd This book is really at the encyclopedia level. The minutiae between the different counting systems of Polynesian body counting systems is of little concern, but this is how precise this book gets. The info is there if its needed.
4th There is no mention of mathematicians, Pythagoreans, ancient trigonometry or algebra in the book, just an expose' of numbering systems. Thw author sticks with numbering systems.
The reader will be in awe of this book's informational overload. I found the secret is to know what to read and what to skim and it makes a rewarding book to give one an appreciation of the numbering system we have today, and surprisingly other systems that have not been entirely retired such as tally sticks, and abacuses.

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. His criticisms doesn't have much real substance and included 'retorts' from other scholars. Dauben brings up Ang and Lam's work, which he himself qualifies as being controversial, to criticize Ifrah's exhaustive work.

In response to Richard Peterson's comment below, Ifrah's book is far too scholarly and encyclopedic to say that it "won't count for as much". If someone else were to attempt the same subject, the result would be a book that is very close to that of Ifrah's book. It is a thoroughly valid work.

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 of themselves as versed in the arts and letters.

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 of and used by a number of different ancient cultures it is very fine.
I specifically liked the picture of an Arabic astrolabe
with 360 degrees on Arabic numbers.
It seems like a long book not to have much of modern interest in it?