On Math, Teaching, and the Magic of Bad Drawings: A Conversation with Ben Orlin

Ben Orlin’s signature stick figures have been (snarkily) explaining mathematical concepts since 2013 at Math with Bad Drawings. By day a math teacher in Birmingham, England, Ben is a voraciously curious, multidisciplinary writer and educator whose work has also been published at The Atlantic, the Los Angeles Times, and Slate.

As a longtime fan of his blog, I wanted to ask Ben about cannibalistic numbers, his passion for teaching, and some of the more egregious uses of math in popular culture — and he was kind enough to respond not only with his sharp words, but also his beloved “bad” drawings.

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All drawings in this interview are courtesy of Ben Orlin.

What is it about math that made you decide to teach it?

When it comes to learning, I’m pretty omnivorous: I’d have happily taught English, history, or social sciences — anything but lab sciences, really. Those are fascinating, but “Biology with Bad Methodology” and “Chemistry with Clumsy Hands” don’t inspire much confidence.

I decided to teach math because it seemed like that was where the action was. So many otherwise-curious people dislike math — even fear or resent it. I like making myself useful, and math education seemed like a place I could do that.

Why do you think so many people are afraid of math?

Because seven ate nine?

Honestly, I think it’s how every mathematics lesson can feel like a test. “Are you still not getting it?” “Everybody else has finished the exercise.” “Do you need me to explain it again?” Struggling at math makes you feel a little stupid, and that feeling hurts. It’s threatening. You wind up rejecting the subject before it can reject you.

An error isn’t just a blemish we need to erase: it’s the outward signal of some inner thought process.

How do you make your students less afraid of this subject?

Well, to help them gain comfort with mistakes, I make an absolutely prolific number of them myself. Staggering quantities of errors. It’s no easy feat.

I also try, every single lesson, to understand what my students are thinking. An error isn’t just a blemish we need to erase: it’s the outward signal of some inner thought process. If I can help a student unpack their own thinking, then they’ll learn to inspect ideas more closely, and absorb them more deeply.

You’ve taught both in the US and the UK. Have you observed any differences between students on either side of the pond?

Dialects, man. Zed vs. zee, protractor vs. protractor, exponents vs. indices… I keep a mental list of Americanisms to avoid if I don’t want to trigger a bitter, ten-minute language war with my British students.

But really, kids are kids. They’re great on both sides of the pond. It’s the educational systems that differ. For example, in the US, we do yearlong themed math courses: Algebra, Geometry, Trigonometry, Calculus. But in the UK, it’s all jumbled up; each year is a sampler platter instead of a single dish.

Mathematics is the art of simplification: figuring out which features are essential, and which ones are extraneous.

Some of your most popular posts have shown the beauty and intricacy of math lurking beneath the surface of everyday things (like tac-tac-toe or high-fives). Where else can we find math in our daily lives, hidden in plain sight?

One that I love is subway maps.

At first glance, they’re lousy maps: curved pathways look straight; dramatically different distances look equal; north and south are crudely captured at best. It’s like if you drew a US map where every state was an equal-sized rectangle.

But we all know how clear and useful these maps can be. And when you read them, you’re actually doing topology. You’re disregarding certain geometric features (size of stations, length between stops, precise direction of path, etc.) and honing in on others (specifically, how the stations connect). Mathematics is the art of simplification: figuring out which features are essential, and which ones are extraneous. So subway maps are quintessential math.

It always weirds me out to see math used as thematic gibberish, random collections of words and scribbles meant to intimidate and excite the audience, like old sorcerers’ spells.

I’m sure you see mathematical concepts misused all the time — are there any particularly funny cases you’ve come across lately?

I’ve got a bunch of examples, because not long ago I saw the movie π, which turns out to be a hot jambalaya of total crazy.

First, the protagonist Max proves his mathematical genius by multiplying 322 by 491. But as any mathematician will tell you: that’s not math. As you advance, you work with numbers less, and abstractions more. A strong 15-year-old student is probably quicker at mental math than a 35-year-old mathematician. So there’s your “math is just computation” myth.

Second, a stranger starts spying on Max, because he’s apparently on the cusp of unlocking the universe’s secrets with his math. But when we see what he’s writing, it’s fifth-grade formulas like “A = πr2.” So there’s your “math is exotic and inscrutable” myth.

Then, at the end of the film, when it’s revealed that the secret to existence is a 216-digit number, Max says to his enemies, “You must have already written down every 216-digit number.” But this is totally insane. If you wrote down a trillion trillion trillion numbers every nanosecond since the start of the universe, you would be only 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001% of the way done by now.

That one’s not really a myth, it’s just wildly inaccurate.

I don’t mean to pick on writer-director Darren Aronofsky, who’s made some great movies since. But it always weirds me out to see math used as thematic gibberish, random collections of words and scribbles meant to intimidate and excite the audience, like old sorcerers’ spells. It makes me worry that this is how math always appears to people!

You often tackle other topics with “bad drawings” — like in your widely-circulated post on the Yale admissions process. What other topics are you interested in debunking or unpacking with your humor and visual acumen?

Well, “visual acumen” is a pretty lofty phrase for “keeps a box of sharpies on his desk,” but I’ll take it! I’ve actually got a folder of half-baked ideas-in-progress. Here’s a sample of document titles:

No idea which of these will actually become posts. Probably a few. Maybe none. Time (and my own erratic sense of obligation) will tell.

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Read more from Ben at Math with Bad Drawings, and follow him on Twitter (@benorlin).