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  • The Universe in Zero Words: The Story of Mathematics as Told Through Equations by Dana MacKenzie
  • Phil Dyke
The Universe in Zero Words: The Story of Mathematics as Told Through Equations by Dana MacKenzie. Princeton University Press, Princeton, NJ, U.S.A., 2012. 224 pp., illus. ISBN: 978-0-6911-5282-0; ISBN: 978-1-4008-4168-4.

This is a book about the history of mathematics. It’s a nice title, but although each chapter is headed by an equation, it is really an excuse for some historical mathematical anecdotes. That said, it is brilliantly written, and this reviewer, who has taught historical aspects of mathematics for a number of years, enjoyed the book and learned some details that were unfamiliar. The author possesses a wonderful skill in presenting technical material to those without the facility to understand the mathematics. For those in the mathematics business, it is always enjoyable to see this being done well.

The layout of the book is interesting; it is presented in four sections, with each section containing self-contained chapters, 24 in all. The first section will be accessible to everyone, as it centers on ancient mathematical material, numbers, Pythagoras’s Theorem and simple geometry. The second section goes from solving cubic equations to calculus and Euler’s application of number theory. There is a brave attempt at detailed explanation, but there will be a thinning out of the readership here, like cyclists breaking away from the peloton. Section 3 tackles more advanced stuff; we have some of the works of Gauss, Hamilton and Galois. Strange geometries, solution of algebraic equations, Fermat’s Last Theorem and the analysis of spectra are all here. This is full of difficult concepts, but the analogies and descriptions are, in my view, successful. Finally the author goes for broke and attempts to get through relativity, quantum mechanics, Cantor, Gödel, the incompleteness of mathematics, chaos and financial derivatives. This is understandably less successful, and I think only the previously grabbed will get through all of this material. In summary, a refreshing look at highlights from the history of mathematics and a welcome addition to the literature, written in a very accessible style.

Phil Dyke
Professor of Applied Mathematics, University of Plymouth, U.K. Email: <>.


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