Jordan Ellenberg really wants you to like math. Not math in the sense of calculating a tip or doing your taxes, but math as the path to understanding, math as evidence, math as truth. Hence the title his new book, How Not to Be Wrong: The Power of Mathematical Thinking, which Penguin Press released this week.
Ellenberg is a math evangelist. As he puts it, "Some of us have to be out in front of people, saying why math is important."
His devotion to this cause is manifested in nearly all aspects of his life and his work. He is the Vilas Distinguished Achievement Professor of Mathematics at UW-Madison, and by all accounts he's a star in the department. A leader in the field of number theory, he's won numerous accolades, awards and fellowships, and was recently named to the inaugural class of American Mathematical Society Fellows. Ellenberg came to UW-Madison in 2007, after earning a Ph.D. at Harvard and completing a postdoctoral program at Princeton. Before that, he was a child prodigy in his hometown of Columbia, Md.
But Ellenberg's work as a professor isn't nearly enough to use up his excess enthusiasm for his favorite topic. For that, he discusses math with lay audiences. His work has appeared in Slate, Wired, The Wall Street Journal, The Washington Post, The New York Times and other prominent publications. He has also talked about math on television (The Today Show) and radio (All Things Considered), and now he's written a book, all in service of his grand plan.
I meet with Ellenberg, curious to see if he'll try to recruit me for his cause. He is eager to do so. The first thing we do is have a little math lesson. We use a formula to estimate how many Facebook "friends of friends" I have. An astonishing number, it turns out, and one that would make me change my privacy settings if I hadn't already set my page to "friends only."
We also talk about the origins of "Do the Math," his popular Slate column, which he started writing in 2002. His comments turn once more into evidence about people's desire for understanding.
"Slate was ahead of its time in wanting to do a regular feature about mathematics," Ellenberg says. "Nowadays lots of magazines and websites want to offer articles about things like data-driven analysis, but back then there wasn't much of it. I think there is a real hunger, a demand from readers to learn about this stuff."
Worlds of inquiry
Ellenberg's specialty within mathematics is called number theory. He describes it as "what people think of when they think about math: addition and subtraction and multiplication, all the things you can do with numbers."
"But haven't we already figured all that stuff out?" I ask.
Ellenberg laughs. "We know nothing. Right now we are standing in a tiny circle of light around our feet, and every 1,000 years, we push that circle out just a little bit. Every time someone sticks his toe out beyond that circle, it opens up whole worlds of inquiry."
Number theory is also the oldest branch of mathematics, dating back to ancient Greece and even earlier. Ellenberg likes being the latest in this long procession of thinkers.
"You've got this line of people stretching back centuries who have all been working on the same things, just handing the ball forward to the next generation," he says.
He clearly relishes his turn on the field.
Ellenberg is also quite funny. He displays a disarming sense of humor about his time as a child prodigy. The son of two statisticians, he showed an early aptitude for math that his parents were happy to nurture.
"When I was in third grade, I started working with a local high school math teacher, and he let me sit in on his math classes," he says. "So when I was 8, I was in this class with a bunch of ninth-graders, and it was fun. They liked me, and I liked them. But what I really wanted was to have my own locker, because lockers were cool."
The path to academia revealed itself quickly, but the path to publishing emerged later. Several years ago, Ellenberg's Slate columns led him to a literary agent.
"Once a year, this guy would call me and ask me if I was ready to write a book yet, but for a long time I wasn't," he says.
But when sabbatical time rolled around, Ellenberg decided he was ready to try it. With financial support from a Romnes Faculty Fellowship and an office provided by the Wisconsin Institutes for Discovery, Ellenberg spent the 2011-2012 academic year writing How Not to Be Wrong.
Once again, his enthusiasm bubbled over. How Not to Be Wrong ended up being much longer than he had estimated. Luckily, his publisher didn't seem to mind.
Ellenberg enjoyed the collaborative atmosphere he found at WID, and he especially enjoyed the chance to consult with resident cartoonist Lynda Barry, who encouraged him to use his own quirky hand-drawn illustrations in the book rather than hire an artist to redo them.
How Not to Be Wrong isn't just for math geeks. Ellenberg's writing is accessible and friendly. In one chapter, he deconstructs the methods several MIT students used to scam the Massachusetts State Lottery. In another, called "Dead Fish Don't Read Minds," he examines the ways scientific data are analyzed, vetted and reported. This essay made me doubt everything I thought I knew about the reliability of scientific reporting.
That is exactly Ellenberg's goal. Armed with an understanding of the math behind things like new obesity studies and unemployment reports, you can draw your own conclusions. You will no longer be constrained by others' interpretations. If you do your own math, you won't be misled.
Ellenberg's nimble, entertaining prose makes a strong case for getting comfortable with numbers. It's clear that math isn't his only gift. Before embarking on his Ph.D. at Harvard, he spent a year studying fiction writing at Johns Hopkins University. There he wrote a novel, The Grasshopper King, which was published by Coffee House Press. Surprisingly, it isn't about math.
The author doesn't seem to have plans to return to general fiction. He says one of the most important things he learned during the creative writing program was how much he missed doing math.
I ask him to comment on the perception that math and science are somehow in opposition to the arts. Ellenberg scoffs at this idea, pointing out that mathematical ideas have always been examined through writing.
"Math is made of words: explanations, arguments, discussions," he says.
He reminds me of how many people are writing interesting things about math. He cites Michael Lewis, whose popular book Moneyball showed how the creative use of baseball statistics could transform a losing team. And fittingly for a former child prodigy, Ellenberg mentions Norton Juster, whose children's book The Phantom Tollbooth is a favorite among nerds (and non-nerds, too).
Ellenberg makes math fun while illustrating its importance. In the introduction and conclusion to How Not to Be Wrong, he talks to an imaginary student, a skeptic who voices the age-old question posed by math students everywhere: "When will I use this information?"
His answer, in short, is that you will use math constantly.
"The lessons of mathematics are simple ones, and there are no numbers in them: that there is structure in the world; that we can hope to understand some of it and not just gape at what our senses present to us; that our intuition is stronger with a formal exoskeleton than without one. Every time you observe that more of a good thing is not always better; or you remember that improbable things happen a lot, given enough chances...you are doing mathematics....You've been using mathematics since you were born."
But that's not all. The other key takeaway is that humans have a responsibility when it comes to math. With knowledge comes power.
As Ellenberg exhorts us: "Use it well."
The Iron Man theory of math
Math is like an atomic-powered prosthesis that you attach to your common sense, vastly multiplying its reach and strength. Despite the power of mathematics, and despite its sometimes forbidding notation and abstraction, the actual mental work involved is little different from the way we think about more down-to-earth problems. I find it helpful to keep in mind an image of Iron Man punching a hole through a brick wall. On the one hand, the actual wall-breaking force is being supplied, not by Tony Stark's muscles, but by a series of exquisitely synchronized servomechanisms powered by a compact beta particle generator. On the other hand, from Tony Stark's point of view, what he is doing is punching a wall, exactly as he would without the armor. Only much, much harder.
To paraphrase Clausewitz: Mathematics is the extension of common sense by other means.
-- An excerpt from How Not to Be Wrong by Jordan Ellenberg