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Enlightening Symbols: A Short History of Mathematical Notation

by Joseph Mazur
Princeton University Press, Princeton, NJ, 2014
312 pp., illus. 38 b/w. Trade, $29.95
ISBN: 9780691154633

Reviewed by Phil Dyke

From the outset let me say that this is a good book.  It is well written by an experienced author and is full of interesting facts about how the symbols used in mathematics have arisen.  It would certainly interest anyone who studies the history of mathematics.   Even for the enthusiast, however, there is danger as the topic lends itself to being a list of facts.  This author avoids this trap mostly through his engaging style but also by breaking the book into short chapters, 24 of them, and avoiding being completely chronological.  The first collection of chapters concerns the origins of the numerals themselves, some origins are of course shrouded in obscurity and controversy, and where this is the case the alternatives are honestly treated by the author.  The second collection is about algebra and is consequently more about the culture of development and use.  This contains a wealth of information and strays into anthropology and religion including more of the beliefs of the author.  Researching some of the origins of algebra remains an active area and new forensic techniques are helping to disentangle who did what when.  The third and final section on the power of symbols is more philosophical and, dare I say, a little bit self-indulgent.  It is still a good read though.  For pedants, some errors are present; I spotted that on page 139 there is a reference to Gauss using the imaginary unit in 1867.  This is supernatural, as he died in 1855.  There are probably others but this does not detract from the book as facts can always easily be checked in this internet age.  What we have here is a scholarly book written by an author in command of his subject.

The book is well structured and the short chapters make it a useful reference book for scholars.  It is written for the layman, but some knowledge of algebra and complex numbers is useful; the lack of which would not prevent understanding or enjoyment but might detract potential readers from picking this as a holiday read.

Last Updated 29th August 2014 2013

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