As the title suggests, the “gimmick” of this book is that each section centers around some particular equation, chosen for its beauty and depth. But it’s less a book about equations than it is simply an engaging tour through the history of mathematics. The writing is wonderful, and it contains a wealth of material, not only of purely mathematical interest but historical and social as well. I honestly couldn’t put it down! I should also mention that the design is stunning—I’m always quite impressed by the quality of Princeton University Press’s design, and this book is no exception.
Mackenzie does a great job explaining the mathematics to a popular audience without “dumbing things down”: he explains things in a way that is clear and simple but still accurate. I only had a few minor factual quibbles, and for the most part they were about subtle issues closely related to my field. (For example, near the beginning of the book he writes that Gödel showed set theory can’t be proven consistent, whereas Gödel actually proved that set theory can’t prove itself consistent—an important distinction. Though later when he actually talks about Gödel in more detail he gets it right.) But for the vast majority of the book I didn’t have any quibbles at all—quite impressive, especially given the book’s committment to present actual equations! Unlike the last book I reviewed, this one really is accessible, and, I think, appealing, to a very wide audience. If you want to convince someone that mathematics can be beautiful—that equations are not just scary things impossible to understand—give them this book!