Review of One to Nine: The Inner Life of Numbers by Andrew Hodges

This is perhaps the first time I have condemned a book for its concept but applauded it for its content. Writing a book that examines the integers 1 to 9 on a per-chapter basis is just silly. It's also impossible; the properties of these numbers are inextricably bound up in the properties of all other numbers. Andrew Hodges knows this, and indeed makes no attempt to conceal the fact that the structure of this book is a lie. In each chapter, Hodges gleefully digresses into topics that have only the most tenuous of connections to their titular number.

Some of these topics are very interesting and worthy of entire books in their own right. Hodges covers electromagnetism, quantum chromodynamics, Fermat, Fibonacci, and some cryptography too. But One to Nine's incredible breadth is, somewhat predictably, also a weakness. Hodges provides able summaries of these topics, but in his whirlwind tour of the first nine positive integers, he can't cover the topics in much depth. Although Hodges' explanations of some fairly complicated mathematical concepts are accessible, I don't think people would find them very helpful.

It doesn't help that Hodges jumps from topic to topic, and even from thought to thought, with the pace of a frenzied beaver on speed. And while I've never been high, reading parts of this book made me feel like I imagine being high would feel: "to consider Two-ness is to confront broken symmetries in a world crammed with them." Um … OK, sure. "Two-ness?" Really? Hodges' writing is a bizarre mix of airy and wistful. His attempts to come off as jaunty are merely jarring, owing to his constant transitions from one topic to another. And, oh my, I have never seen so many rhetorical questions in my life. Excess and superfluous much?

As a result, Hodges undermines the very effect essential to a popular mathematics text: the sense of wonder that mathematics evokes. He tries for it, and once in a while gets close. But before the monotonous tour guide can say, "And we're moving…" Hodges has gone off on a parallel track, and you're forced to catch up rather than stick around and appreciate the beauty of what's just been covered. One to Nine did little to augment my admiration of number (and much diminished any remaining shred of interest in Sudoku).

Hodges also makes sporadic references to Desperate Housewives, climate change, and Alan Turing. Alan Turing, I can understand, because his contributions to cryptography, computer science, and mathematics are pretty important. That doesn't quite justify Hodges' obvious hero worship, however. While mathematics has a role to play in answering questions about climate change, Hodges never actually addresses that role. Climate change just gets mentioned, much like Desperate Housewives (allusions to which I am at a loss to explain at all).

Then in the last chapter, the book abruptly shifts from its focus on the properties of number into a polemic about mathematics in education and how Alan Turing met an untimely end. In both cases, Hodges makes some good points. Yet I don't appreciate being ambushed by such arguments at the end of the last chapter of the book.

All of this makes for a rather dense barrier to the main event. It's clear that Hodges knows what he's talking about. He just didn't convince me of his ability to talk about it well. Nevertheless, despite his meandering through the mathematics, Hodges does make it possible to eke a semblance of erudition from this book. I'm not sure it's worth the effort. One to Nine is by no means a bad book, but it does not excite me or delight me in the way that a book like A Short History of Nearly Everything does.

Maybe it needed more Two-ness.