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The Math Book: From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics

Clifford A. Pickover
Publication Date: 
Number of Pages: 
[Reviewed by
Fabio Mainardi
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From the author’s introduction: “…I hope to give readers a taste for mathematics using few formulas, while stretching and exercising imagination.” That means that this book is not addressed primarily to mathematicians (whose taste for mathematics is already well-developed!). It is intended for a recreational reading, and not as a treatise on the history of mathematics.

Here is how the contents are organized: each topic occupies two pages, a few paragraphs on the left and a very nice illustration on the right page. The entries are in chronological order; nevertheless, one can jump quite freely from one topic to another without losing much. Of course, most of the topics would deserve a whole book on their own! A bibliography is compiled, however, for further reading.

Again from the introduction: “My goal in writing The Math Book is to provide a wide audience with a brief guide to important mathematical ideas and thinkers, with entries short enough to digest in a few minutes. Most entries are ones that interest me personally. Alas, not all of the great mathematical milestones are included in this book…” Among the excluded milestones, I would mention:

  • the simplex algorithm;
  • the Black-Scholes equation;
  • Markov chains and their application to the Web;
  • the p-adic numbers.

Conversely, not all the chosen entries can be considered milestones in mathematics:  the American TV show NUMB3RS, for instance, obtained a place in the book because, according to the author, has created many learning opportunities for students. Once again, I will cite the (very honest) introduction: “This is not a comprehensive or scholarly dissertation, but rather is intended as recreational reading for students and interested laypeople.” The objective being the popularization of mathematics to a wide non-specialized audience, one cannot reproach the book for not being deep enough, nor for the inclusion of “light” moments. Technical explanations and formulas are avoided in order to reach an audience as wide as possible. (Alas, there is a misprint on one of the formulas that do appear: on page 472, the defining equation of the Mandelbrot set should be read \(z_{n+1} = z_n^{2} + c\); the square is missing in the book.) Some space is dedicated to puzzles and games, some of which, I’m ashamed to say, I had never heard of; others, like Mastermind or Tetris, have amused millions of people all around the worlds in the last decades.

What the reader will gain is, I think, a panoramic view of the world of mathematics and its applications, as a beautiful fairy landscape. Mathematics is hard and the work of mathematicians is often misunderstood and not fully appreciated, so any effort of divulgation is more than welcome.

The author welcomes feedback and suggestions for improvement from readers, and a forum dedicated to this aim is hosted at

Fabio Mainardi earned a PhD in Mathematics at the University of Paris 13. His research interests are mainly Iwasawa theory, p-adic L-functions and the arithmetic of automorphic forms. At present, he works in a "classe préparatoire" in Geneva. He may be reached at

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