The Invisible Power of Mathematics

The Invisible Power of Mathematics by Giovanni Samaey and Joos Vandewalle discusses 20 wide-ranging applications of mathematics, devoting an average of eight pages to each application. To cover so much ground in so few pages, the discussion is necessarily not very detailed. The book feels like a series of conversations about mathematics while walking through the woods with nothing to write on and with far more words than equations.

Mathematics books have a continuum of levels of detail, with Principia Mathematica by Alfred North Whitehead and Bertrand Russell on one end of the spectrum and something like Men of Mathematics by E. T. Bell on the other. Hardly anyone wants to read books on Whitehead and Russell's end of the spectrum, though mathematicians usually want a little more detail than given on Bell's end. The Invisible Power of Mathematics is closer to the Bell end, which is needed given book's intended purpose. The authors state in the preface:

This is explicitly not a mathematics book, but a book about the role mathematics plays in devising the creative solutions the world needs. (Emphasis in the original.)

The book does contain inserts with more mathematical detail, though not a great deal of detail.

A few of the applications presented in the book are commonly found in popular accounts of mathematics. For example, the first two chapters discuss public key cryptography and small-world networks. But most of the applications are not nearly so familiar. For example, there is a chapter on the problem of redistributing bicycles around a city, which is related to the optimal transport problem and earth mover's distance. The last third of the book is devoted to contemporary issues such as driverless cars and pandemics.

The book's subtitle is The Pervasive Impact of Mathematical Engineering in Everyday Life. The breadth of examples supports the claim that applications of mathematics are pervasive. A thin book with such breadth of content must necessarily avoid going into much technical detail. But as the authors say, this is not a mathematics book per se but a book about mathematics and its application to familiar things.

 John D. Cook is an independent consultant in mathematics applied to data privacy.