The Number Mysteries: A Mathematical Odyssey through Everyday Life [Paperback]

I have previously read and reviewed Rob Eastaway's books Why Do Buses Come in Threes? and How Long Is a Piece of String? on The hidden mathematics of everyday life, but although I've been aware of Marcus Du Sautoy's books for some time, this is the first I've actually bought and read. While his approach is different from Rob's, Marcus also has a way of explaining mathematics such that it can appeal to the wider public. The book is divided into five chapters, the basic themes being prime numbers, geometric shapes, winning streaks, coded information and predicting the future.

Perhaps the most amusing subject in the first chapter is the life-cycle of cicadas, which are apparently 7, 13 or 17 years in duration, depending on the species. The author suggests this cycle using one of three prime numbers may be a way of discouraging predators, but as he`s a mathematician rather than a biologist, I won`t assume that although it sounds plausible.

Sometimes the author strays from the chapter heading but that's no problem. For example, the first chapter discusses Fibonacci numbers (and the inevitable example of breeding rabbits) as well as prime numbers. Another off-topic digression that I found interesting was the author's discussion of the early number systems developed by ancient civilizations.

The chapter on geometric shapes is another fascinating chapter, discussing the shapes of footballs, teabags, snowflakes, coastlines, viruses and abstract paintings among other things. Golf balls aren't featured here; they come later in the book. The chapter on winning streaks discusses a variety of games and puzzles including the 18th century Königsberg bridge puzzle. Rob Eastaway also covered this puzzle in one of his books; it seems to be regarded as a particularly significant example in the world of mathematics. Marcus tells us how Königsberg has changed including the bridges.

The chapter on coded information explains that some codes appear to be uncrackable because they use very large prime numbers as multipliers, but also discusses other codes. The designers of the German Enigma code thought it was uncrackable, but British mathematicians eventually proved them wrong. There are other codes that were never meant to be secret, including the Morse code invented in the nineteenth century. The author also discusses check digits, using the ISBN book cataloguing system as an example. The last chapter on predicting the future discusses pendulums, boomerangs and weather among other things.

This is a very entertaining book although it does get a little technical here and there. As such, anybody who is in the least bit intimidated by mathematics might be better to begin with one of Rob Eastaway's books. However, I like both authors in different ways and I may end up buying more books by both authors.

Marcus du Sautoy is a professor of mathematics at the University of Oxford. He also has appeared on television programs presenting mathematical subjects for general lay audiences. In THE NUMBER MYSTERIES du Sautoy tries to do much the same thing - to show a general lay audience how mathematics underlies or explains much of everyday life: from the number of petals on a flower, to dragon noodles, to the construction of soccer balls, to three-dimensional teabags, to the Beijing Olympic Swimming Center, to roulette wheels, to Sudoku, to the Mayan calendar, to the ISBN code number for this book and all others published since about 1970. Along the way, he discusses such mathematical concepts as perfect numbers, Fibonacci numbers, fractals, and prime number codes.

Du Sautoy is enthusiastic and obviously knowledgeable. His writing style is relatively informal and, for the most part, comprehensible by the moderately intelligent and interested layperson. But I sense that the audience for THE NUMBER MYSTERIES is somewhat limited. The book surely is too simple or superficial for those who already have a strong background in mathematics. As for those with little or no interest in mathematics, I doubt that the book will kindle one. So it appears that its audience will be primarily those who once were charmed by the rigor and mystery of mathematics but who have lost touch with the discipline - and rather regret that development of life.

I count myself in that group, so I like reading a book like this every few years. Among its ilk, I found THE NUMBER MYSTERIES to be in the middle of the pack. One complaint I have is that the book does not include, for those who are intrigued by one or more of the mathematical concepts mentioned in it, references for further, more in-depth study. Another complaint, albeit having nothing whatsoever to do with its content, is that the cover of the paperback edition is downright ugly; it is perhaps the most unsightly book cover in my library.

I really enjoy popular science and math books in general, and I'm enjoying this one in particular. My criticism though is that Du Sautoy is not a master of language or explanation; he's only pretty good. I'll give two examples:

1) Foam. Du Sautoy starts talking about foam in his section on the geometry of bubbles, and tells us that foam is a thorny mathematical problem, but he never tells us what foam is exactly. I read through about half of this section before I figured out what problem it was about foam that Du Sautoy was solving. A better writer would have made that clear from the beginning. This is the sentence Du Sautoy needed to write but didn't:

"Foam is a trickier problem than the simple case of two bubbles sticking together because foam is made of thousands of bubbles of different sizes sticking together in one mass. Thus, on the inside of foam, all of the bubbles are plane-sided; no bubbles have a spherical portion. The problem of foam is figuring out what the precise three-dimensional shape of all those tiny bubbles inside foam is, because there must be one most efficient shape for plane-sided bubbles to take when they are packed together like that, i.e., one most efficient way for three dimensional solids to pack together perfectly. We know that nature will automatically form bubbles of whatever that efficient shape is, just like a bubble will take a perfectly spherical shape when it is on its own."

2) Here's a sentence I still don't understand, from the same chapter on three-dimensional shapes, about wrapping two ropes around a bagel shaped solid:

"If the black rope is wrapped through the inside of the hole of the bagel and the white rope is laid down on a circle going around the outside ring of the bagel, then there is no way to pull the black rope to match up with the white rope without cutting it."

This is the main payoff sentence to a puzzle that takes 2 1/2 pages to describe. I understand everything else about the puzzle, before and after. I just don't understand this. In particular, what does "pull the black rope" mean, and what does "match up with the white rope" mean? Likely, someone will explain this to me in the comments of this review and I'll get it, but the point stands: these phrase are far too vague on their own to do the job of explanation they are intended to do.

There's just something slightly off about the way Du Sautoy writes; he isn't in our heads as readers, and doesn't realize when he hasn't built the bridges to understanding. I quite enjoy reading about math. I loved Simon Singh's book on Fermat's last theorem, and was able to follow his presentation of the proof all the way through to the best of my ability. Same with Douglas Hofstadter's presentation of Godel in "I Am A Strange Loop". So I have to lay the gaps in understanding of the simple problems presented in this book at Du Sautoy's feet, and not my own.

All that said, the book is still a bucket of fun. I enjoyed every page.