The Universal History of Numbers (Paperback)

Mathematics: From the Birth of Numbers by J Gullberg  (32)  £39.90

Numbers: Their History and Meaning: Their History and Meaning by Graham Flegg £12.59

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Amazon.co.uk Review
For those of you who have read Georges Ifrah's first book, The Universal History of Numbers: From Prehistory to the Invention of the Computer, this is the third of a two-volume set! Just to clarify this, the first volume is being split into two and, together with this new third volume, republished as a trilogy. For those of you who have not read the first book, volume III begins with what could have been a very useful "Chronological Summary" and a "Recapitulation" of the ideas expressed in the first book. Unfortunately, without a preface or introduction, the unwary reader is immediately confronted with a very condensed version of the first book. Indeed, Ifrah's detailed study of number systems, when reduced to a series of illustrated plates, gives the impression that the history of numbers is little more than a history of typography. Yet another "Chronological Summary" from Calculation to Calculus follows, thereby reinforcing the feeling that the book is a collection of notes waiting to be crafted into a strong narrative. The translator, the unsung hero in many publications, has done sterling work in adding copious notes and helpful cross-references. The initial feeling remains, however, that this is a collection of jewels without a crown.

Having said that, the scope of the book is enormous, tracing the history of calculators and computers, from mechanical to electronic devices through both analogue and digital incarnations. There are some familiar faces, such as Pascal, Babbage, von Neumann and Turing, as well as many others who have so far escaped the spotlight. As a reference work it has a good index and an extensive bibliography. The author acknowledges regret at the lack of illustrations but gives references to such sources. In the search for universality and completeness it has, however, forsaken a strong guiding theme. The most engaging sections are where the mathematics, history and technology come together, bound by personal ambitions, whether intellectual or financial. In such sections Ifrah pauses from being a cataloguer to indulge in some story telling. It is here that the nuts and bolts of technology come to life. For teachers, students and researchers, this will prove to be a very useful starting point into a fascinating area of human innovation. But one would venture that this is a work destined for the library shelves rather than the bedside table. --Richard Mankiewicz --This text refers to the Paperback edition.

Amazon.co.uk Review
This is an extraordinary book by an extraordinary author. Mathematics teacher Georges Ifrah spent a decade travelling around the world researching the origins of numbers, supporting himself by working as a waiter, taxi-driver and night clerk. The result is The Universal History of Numbers, an impressively detailed account of pretty much every aspect of the emergence and evolution of counting from the Cro-Magnons of 25,000 BC through Babylonian, Greek and Roman times to the metric system and beyond.

Ifrah never misses a chance to include intriguing insights that any reader can appreciate, from how to form cuneiform numbers on wet clay to performing calculations on your fingers--or how to use a Chinese abacus (with details of a 1945 competition between an abacus expert and someone using a calculator; the abacus-user won easily).

Much of this detail may well prove wearisome, however. I for one would have appreciated much less on long-dead number systems, and much more on modern developments in numbers. There is very little coverage of such key issues as irrational and transcendental numbers