Math Is Cool! And So Am I! No, Really!

I try to post blogs only about works that make me feel something strongly, whether that something is outrage or admiration, melancholy or joy. Today, I’ve decided to go with “joy”. And that means… math!

I know there are tons of shows and cartoons and public service announcements out there that try to convince you that math is cool and knowledge is power, and stay in school, kids! And there are billion others that try to sell you on the idea that math isn’t cool, but it sure is useful, so you better get cracking.

OK, it’s true that it’s nice to be able to figure out who should pay what to whom when you eat out with friends, or how much your income tax comes to. And, if you’re an engineer or scientist or economist, you’re going to need those formulas to figure out the information you require.

But the math I like isn’t like any of those things. It’s not about memorizing multiplication tables or finding the area of a shape or even taking the integral of a function. It’s about the basic, fundamental stuff that makes up the brains of human beings. So, you see, I don’t buy the idea that math is something only really smart people can do and/or like, that there’s something intrinsically less “human” or “creative” about it than, say, writing a story or figuring out the meaning of life. Because what math is basically about is this: hey, we have these things called numbers. What sort of things are they, and what sort of patterns can we find in them?

If you have some math background, you might think at first that I’m reducing all of math to number theory – not so! OK, it’s true, number theory is the branch of mathematics that best matches the description I just gave: what are the properties of numbers and what can we do with them? But calculus is basically the same idea: I have numbers of a certain form (say, 1/x), and I am going to add every single one of them together where x goes from 1 to 2. What do I get*?

I think what turns a lot of people off about math is the prevalent idea that you either “get it” or you don’t. It’s not like English or geography or history, where even if you don’t quite understand, you can still make passable or interesting arguments. There’s a right answer and a wrong answer in math, which some people take to mean that there’s a right sort of person and a wrong sort of person to do math. If you get the answers wrong, you’re the wrong sort of person, and maybe you should try something “easier”, like English.

(That last attitude in the scare quotes, by the way, is part of the reason I detest the “math is so hard and only for really smart people!” attitude. Because when you throw math and science all out of proportion as “super-duper difficult” things, you tend to turn the humanities into “subjects dumb people do because they can’t handle math and science”, or, worse, “subjects that, OK, aren’t so hard, but YOU just don’t get them, because you can’t FEEL the way I do”. As someone who’s done university courses in both the sciences and the arts, and as someone who is now working in a field where she sometimes has to TA classes of mixed science and humanities students, I think this is completely false. It’s true that it’s much easier to get a  mediocre mark in the arts than the sciences, and much more difficult to fail drama than math. But it’s also true that it’s a lot easier (despite there being a lot of hard work involved) to be an excellent science student than it is to be an excellent arts student. Perfect math quizzes are relatively commonplace; perfect essays, not so much.)

IMO, this right person/wrong person attitude is completely wrong-headed, but I think it’s pervasive because most people are taught that the point of math is to get the Right Answer. The reason for this is obvious: you don’t get points on a test for getting the ‘wrong’ answer; math is not useful for building bridges or deciding how much paint you need to redo your dining room if your figures don’t turn out. And, hey, being useful’s what math’s for, right?

Wrong. Math is useful, but that’s not all math is. It’s also creative. And open-ended. And artistic.

True, in high school and elementary school, most math isn’t like this. I know from being a tutorial assistant for first-year calculus that an unfortunate number of math students are taught to do whatever it takes to get the right answer, and if that means memorizing a formula without understanding it, then memorize away. But all that stuff – all the formulae for calculating area and rules of operations – is prep work for what mathematics is all about.

Sure, there are mathematicians right now who are working on problems that have a definite, numerical solution. But there are also mathematicians working on methods, on definitions, even on philosophy. In research mathematics, there is no formula to plug in and no penalty for not using the methods in the book. You have a problem, and you can try to tackle it any way you want, as long as it makes sense. Sometimes you’re aiming for a number or a formula; sometimes, you’d be glad to have an estimate; other times, all you’re trying to show is that there is an answer to the problem in the first place.

Math is arithmetic like 1+1=2, but it’s also theorems about what we can prove, like the work of Kurt Godel, or inventions of whole new worlds where parallel lines always meet, like the work of Bolyai, Lobachevsky, and Riemann. Think for a second about the number 3. What is 3? Is there a way to describe it that isn’t just an example of three objects**?

Okay, I realize that some people just won’t like math, no matter what kind it is – a times-table worksheet or an elegant treatise on how ten logical people trying to figure out whether they’re wearing white hats or black hats can come to a conclusion. And that’s cool. Some people don’t like English, history, or philosophy. But the idea that disliking math somehow makes you more human, more creative, or more “real” –  I think that’s just not so***.

* Answer: ln2

** Answer: Yes, yes, there is, but to find it, you’ll have to read an elementary text on set theory or the work of Bertrand Russell.

*** There seems to be a common notion that I very much dislike that the only “real” or “true” part of a person (their soul, for shorthand, I suppose) is the emotional part. That seems ridiculous to me – if the thing that’s thinking this isn’t a “true” part of “me”, then what the heck is it? Can we even separate thinking and feeling like they’re two completely different things? I doubt it.