janmr blog

Book Review: The Book of Numbers

The Book of Numbers is a wonderful book about, well, numbers. And lots of them. From ancient ways of writing numbers to Gaussian integers to surreal numbers. The authors are some tough mathematicians, too. John H. Conway is Professor of Mathematics at Princeton University, an authority in game theory and group theory, and the inventor of the Game of Life and surreal numbers. Richard K. Guy is professor emeritus of mathematics at the University of Calgary and has (co)authored several hundred publications on combinatorial game theory, number theory and graph theory.

The number of topics in the book is huge. Some of them are listed here, according to the chapters in which they appear:

With this amount of topics and only 300 pages, no topic is treated in depth, some taking up only half a page. But many of the facts stated or questions raised in this book are nontrivial. I found myself repeatedly staring blankly into the air, wondering about some result or comment from the book—or simply thinking that I had to find some more information on this subject. And that is, in my opinion, a great quality for a math book. Each chapter finishes with a list of references, so the reader has some starting points for further material.

It should be noted that each chapter can be read independently of the others. So you should be able to dive into a single chapter without reading the previous chapter.

You have to have some knowledge of mathematics to enjoy this book. The first chapter (on different number systems and ways to write numbers) is mostly pure text. But the subsequent chapters are mostly formulas and figures, facts and theorems. A high school mathematics level, or equivalent, should be sufficient to enjoy most of the book, though.

It was a joy to read this book. I highly recommend it.

Book facts: