Image: “maths” by Sean MacEntee on flickr.

When I tell people that I’m a math major, I usually get one of these reactions:

1. Oh, I’m so bad at math. You must be really smart. Ha ha.
2. Are you going to become a teacher? I hated my math teacher.
3. Why?!
4. EEEEEWWWWWWWWWWW
5. Me too.

I actually once had someone get up and run away when he saw the math on my computer screen. Not kidding. He came back, but still.

This is an open letter to anyone with reactions 1-4:

You’re not bad at math. Even if you hate it. Even if you flunked it in high school.

“We aren’t really going to use numbers much in this class”

On my second day of Queens College, I was scheduled to take a class called Honors Calculus. I got lost on the way there.

As a scared freshman, this was not a fun experience. My friend and I wandered Kiely Hall, asking confident-looking students for directions. Finally, we found out that the building has a basement, which, delightfully, can’t be accessed from 80% of the staircases. All right then.

When we finally got there, we were greeted by our new professor, a high-energy guy with spiky black hair. Most of my classmates were freshmen, like me, and most of us were honors students who had gotten good math grades in high school.

One student asked the professor which calculator he should get for the class – was a TI-86 okay?

The professor looked a bit confused, smiled a little, and said, “No calculator.”

Why no calculator?

“We aren’t really going to use numbers much in this class.”

At the time, I was shocked. A math class with no numbers? Does that even make sense?

It’s funny for me to look back on that moment. It’s almost cute. Because by now, almost none of my math classes use numbers much.

If this is surprising to you, I get it. But the fact that this is a surprise points to a huge gap in many people’s education. It’s the gap between what we learn in math class and what math actually is.

What it Takes to Be Good At Math

Here are some qualities that seem really important in, say, high school calculus:

• Memory
• Following directions
• Quick thinking

In contrast, here are the three qualities that have been most important for me in doing math well:

• Curiosity
• Enjoying abstract reasoning (like logic and puzzles)
• Persistence

This, I think, confuses people. Standardized elementary and high school education makes us think that math is about drills, repetition, and memorization. But good mathematics — real mathematics — involves next to none of that.

When someone says to me, “I’m bad at math,” what they usually mean is that they’re bad at drills. They probably struggle to get the “right” answer when someone asks them to compute something. It seems, based on the horrified face that I often see people make at the word “math,” that elementary school math class constituted some sort of awful trauma.

Imagine if you grew up going to a school with mandatory music class. The class required you to memorize sheet music. You had to reproduce that sheet music for homework. Maybe you had to study rules and patterns in sheet music. You had to apply those patterns to fill in music notes on exams.

Now imagine you had to do all of that, but had never actually heard music.

This is, unfortunately, a close analogue to many people’s experience in math class. We frequently are told what the rules are, copy them, and apply them to different numbers, but we never get to hear the music. The motivation for it all — the why anyone even cares about math — is too often buried under computations.

By now, I almost never compute things the way I did in elementary or high school. I don’t plug things into formulas. I don’t move numbers and variables around the page unless I care about what those variables mean. My homework sets look like essays, with splashes of jargon and Greek. I think it may be that the current educational system has buried the things that make math compelling. When we focus on drills and computation, we lose out on math’s aesthetic qualities, its synchrony with the natural world, and the fact that it’s fun.

Math in Plain English

I’ve been blogging about math for two years now. Some of my posts have been philosophical, about the nature of math, like Is Math Fiction? Some were meant to clear up misconceptions, like What “=” Means. And recently I’ve been writing about the relationship between math and computer science, like in Trees, Dictionaries, Pickles, and Loops.

Outside of this blog, I do math research. When I tell people I do math research, I am invariably asked, almost word for word, “How could anyone do math research? Isn’t math done?” And it’s not surprising to me that people think that. The math taught in U.S. high schools is really old. Algebra started with the Babylonians, geometry is from the Ancient Greeks, and even calculus was invented in the 17th century. It’s not bad – it’s here because it’s still good! But there’s new math, that’s happening right now, that no one even hears about.

So my final message for the year is this. There’s a nice thing, a beautiful thing, a deep thing out there. It’s called math. It’s got a bad rep. People think they know what it is, but what they know as “math” is not what math actually is.

I’m not going to try to say exactly what math is here — I’ve tackled that before, in posts like Is Math Fiction?, Math Backwards, and On Math and Meditation. I will say this, however. Being “bad at math” is like being “bad at museums” or “bad at red wine.” Not everyone enjoys puzzles, concepts, or abstract ideas in the same way. It can just take some time to learn how to appreciate them.

In your life, even if you think you hate math, you likely have had good experiences with it, because fun math is all over the place. You may simply not have recognized it as math. I hope my blog has given you some idea of what math is and how to access it. I hope I’ve shared some glimpses of math that anyone can partake of and enjoy. Yes, there’s a high barrier to entry. You have to work a lot to get to the point where mathematics is like listening to a symphony. But if there’s one thing I’ve tried to show with this blog, it’s that real math is more than — maybe entirely different from — what gets taught in math class. Real math can get hidden when generations of curriculums emphasize computation over mathematical thinking.

I’ve been lucky enough to find out about some beautiful math in the last few years. I’ve tried to put it into plain English so you can enjoy some of what I’ve discovered.