“If one man more than another is to be credited with starting the mathematical and physical sciences on their course from antiquity to the present it is Pythagoras.” So says E. T. Bell at the beginning of the Chapter 9 of this book. Indeed, as we go on into the book it becomes clear that the hero of The Magic of Numbers is actually Pythagoras.
In the book under review Bell discusses Pythagoras’ numerology as an initial and basic part of the central idea that “Everything is Number.” He tries to follow the footprints of this opinion in the works of great mathematicians and physicists in ancient and modern times. Along the way he expands on the meaning of “everything” in the phrase. For example, on page 160 he writes, “If everything is number as Pythagoras asserted, it must be possible to prove that all space is number. The Pythagoreans accomplished this by…”
At the beginning of the book is a nice (imaginary, of course) portrait of its hero, by Raphael. Then follow 27 chapters, mainly discussing Pythagoreans view of numbers (not from the point view of number theory, but of numerology), the structure and geometry of the universe, other sciences, and philosophical truths. In the chapter on “The Cosmos as Number” we read: “The heart and brain of the Pythagorean cosmos are the decad and the tetrad. The decad consists of the first ten natural numbers, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and the tetrad of the first four, 1, 2, 3, 4.”.
The book is a really philosophical text including some historical notes. Its main subject is the roots of the idea of using numbers and the effect of this on the growth of the sciences. In one word, the book is about the historical philosophy of “numerology”. Of course, having originally been published in 1946, the book may now be outdated with respect to classical history. I believe that, rather than mathematicians, this book would be more interesting to philosophers, and more specifically for the people interested to know more about numerology.
Mehdi Hassani is a faculty member at the Department of Mathematics, Zanjan University, Iran. His main field of interest is Elementary, Analytic and Probabilistic Number Theory.