I math for a living. I mathed, both amateurly and professionally, at school. I math quite a bit. And as a math teacher, I like reading "pop math" books that try to do for math what many science writers have done for science. So picking up How Not to Be Wrong was a no-brainer when I saw it on that bookstore shelf. I’ve read and enjoyed some of Jordan Ellenberg’s columns on Slate and elsewhere (some of them appear or are adapted as chapters of this book). And he doesn’t disappoint.
I should make one thing clear: I mainlined this book like it was the finest heroin. Partly that’s because I just love reading about math, but in this case I was also days away from moving back to Canada from the UK when I started this, and luggage space was at a premium, so I was on a deadline to finish this book. I injected chapters at a time into my veins, revelling in that rush as Ellenberg charismatically and entertainingly explores the math behind a lot of everyday concepts and ideas. Unlike similar attempts, however, Ellenberg doesn’t pull the punches. He’s more than willing to go into the higher-concept ideas behind the math, and when it starts getting too esoteric or academic even for this venue, he’s always ready with a book recommendation for those interested in some further reading.
Early in my reading, I tweeted I had already decided to give this book five stars because Ellenberg alludes to Mean Girls in a footnote. (Specifically, he says, “As Lindsay Lohan would put it, ’the limit does not exist!’”) That’s really all you need to know about Ellenberg’s writing style and sense of humour. Actually, I’m not all that enamoured with the footnotes in general; they interrupted the flow of my reading and the symbols used to mark them were slightly too small, so I kept missing them in the text—but that’s a design issue. The content of the footnotes themselves is often informative or, as in the case above, humorous. Ellenberg might be a university math professor, but he also has a sense of humour and an awareness of pop culture that helps to make his writing accessible.
I’m impressed by the way Ellenberg effortlessly straddles pure and applied mathematics. The child of two statisticians, he clearly has a good grasp and appreciation of the way applied math drives so many areas of society. From economics to gambling, he makes passionate appeals for informed perspectives over simplistic analogies or fallacies. His first chapter criticizes analogies that promote linear thinking about taxation when the very same economists writing these analogies know that taxation probably isn’t linear. He doesn’t argue for or against an increase in taxes, but rather he points out that it’s wrong to oversimplify the concept when trying to sell it to the public. Is a curve really all that much harder to understand than a line?
There’s also some great chapters on odds and the lottery, in which Ellenberg recounts how a group of MIT students set up a legitimate operation to bulk buy lottery tickets from a certain game that actually gave them good odds of winning. They made a profit, because they used math to turn a game of chance into a predictable investment strategy (which is more than we can say for the stock market). So, you know, stay in school kids.
But actually, the parts about the lottery that impressed me were more towards the purer end of the math spectrum. Ellenberg started discussing, for example, how best to pick the numbers on one’s tickets so that one could maximize the chance of winning at each tier of prizes. It turns out that it’s possible to represent the way of picking these numbers geometrically (yes, as in pictures) and that it’s related to the way we create error-correcting codes (which allow us to send instructions to spacecraft, and compress data in JPEGs, MP3s, and on discs). He goes into quite a bit of detail about the more advanced concepts behind these ideas. Later, he points out how correlation on scatter plots corresponds to an ellipse—and we know how to deal with ellipses algebraically, which gives us a good toolset for talking about correlation algebraically too.
So, How Not to Be Wrong makes an effort time and again to belie the impression that we often get in school that math consists of a series of discrete topics: arithmetic, geometry, statistics, and the dreaded algebra. We teach it that way because it’s easier to lay out as a curriculum and focus on the essential skills of each discipline. And also because we are boring. If you’re lucky, like me, then as a student you’ll start to see the connections yourself. Circles and pi start showing up everywhere, to the point where suddenly you feel like you’re being stalked, and no amount of infinite series or integration is going to save you. But really, good teachers start showing these connections as soon as possible. We fail students and leave them behind because, in our rush to equip them with the skills we’ve been told they need, we rob them of the idea that math is a creative process, instead fostering this false impression that math is a sterile, difficult, procedural slog. If it is, then you might be a computer.
Ellenberg never demands a knowledge of integral calculus, of set theory, or of transfinite numbers. What he does demand is an open mind, a willingness to be convinced that not only does math have a useful place in life (it’s pretty obvious to most people that someone needs to know how to math; they just don’t see why it should be them) but that a deeper understanding of the roles and uses of math can enrich anyone’s life. One can be a believer in the power of mathematics without necessarily worshipping at its altar, and it’s this quest for adherents rather than acolytes that makes this popular math book successful. It helps that Ellenberg’s style is witty. It helps that he is passionate without sounding too evangelical. He weaves in enough history, anecdotes, and allusions to demonstrate that mathematicians’ journeys and the development of mathematics as a discipline has been just like everything else in life: alternately dramatic and dull, intense, occasionally acrimonious. We don’t like to admit it, but we mathematicians are people too. And occasionally we’re wrong, very wrong (like those nineteenth-century French eugenicists…). The title here is tongue-in-cheek, and How Not to Be Wrong can’t guarantee your future correctness with great certitude. All it can do is help you think more critically, more logically, but more creatively about the problems and questions that you’ll face in the future. Because mathematics is a tool for helping us to do amazing things. You can be a novice, or you can be a proficient user of this tool, but either way you’ll need to pick it up at some point to do a little handiwork. Don’t fear it: embrace it.
Oh, and read this book.