Okay, it’s true, I did request this book from the library, I did check it out and sit down to read it. But I really had absolutely no idea how much I would enjoy it, and I definitely did not expect to stay up all night because I just didn’t want to put it down.
Jordan Ellenberg, professor of mathematics at the University of Wisconsin-Madison (home of my graduate school, for full disclosure) has written a book about math: not how you learned it in high school, but how it really is, both for professional mathematicians and in the day-to-day world where mathematical thinking is useful. If someone had taught me math like this when I was a kid, I’d be making a whole lot more money than I am right now.
We’re not talking about addition and subtraction here, or even algebra or calculus. Well, a little calculus. And some geometry. But stop, don’t run away, it’s really not that scary. Because mostly what we’re talking about – what Ellenberg is talking about in this book – is the way math works, the way that math shapes the world, and the way we can use math to change the way we interact with the world.
He uses the story of Abraham Wald in the introduction, to suck you in to his way of thinking. Wald was a mathematician working for the military during the Second World War when they came to him with a problem. Here are the planes that come back covered in bullet holes, the generals said. We need you to tell us where to put the armor. The generals were figuring somewhere on the wings, which was where there were more bullet holes than anywhere else. But Wald said, no, you put the armor on the engines. Why? Because the planes with bullet holes in the wings came back. The ones with bullets in the engines? They weren’t flying home at all.
That kind of logic is at the core of what Ellenberg is teaching with this book. And I gotta say, it’s pretty effective. By the end of the book, I understood for the first time the point of purely theoretical math.* Also, I kind of want to play with non-Euclidean geometry. And not in a Lovecraftian way, for once.
As a bonus, Ellenberg is pretty damn entertaining while he’s teaching. Examples range from baseball statistics to politics to con artists, and the book is liberally scattered with amusing footnotes. For example, from a description of how not to add percentages, using the Florida 2000 election as an illustration:
Yes, I, too, know that one guy who thought both Gore and Bush were tools of the capitalist overlords and it didn’t make a difference who won. I am not talking about that guy.
He also uses an XKCD cartoon as an example. So he’s obviously a man of refined and distinguished tastes.
I could get all dramatic and say that this is an important book and everyone should read it because it will help them – to paraphrase the title – be less wrong all the time, but that would sound preachy, and I hate that. Instead I shall say that this is a massively enlightening and entertaining book, and if you like having your mind blown but always suffered through trig by looking things up in the back of the book and praying you’d remember the formulas long enough to get through the test, you might enjoy How Not To Be Wrong more than you might think.
*It’s because math is based on a very few basic principles, out of which you can create complex structures, but because there are so few building blocks those complex structures tend to generalize well. So you do some math to describe one thing, and then you elaborate on that math in a purely theoretical way, and then it turns out that the same math describes a completely different thing. Which is kind of mind-blowing, really.