Jeremy Côté

Mathematics for Enjoyment

The title of this post may not be words you are used to seeing together. Sure, you might think that mathematics is powerful, but does anyone actually do mathematics just because they enjoy it? If you ask someone other than a mathematician, you might expect the answer to be “no”.

If you ask someone if they enjoy mathematics, there tend to be two possible answers that are given. The least common answer is, “Yes, I’m pretty good at mathematics.” The more common answer is, “No, I’m just not good at mathematics. It’s not for me.”

The astute reader will notice that both of these answers don’t really address the question. Instead, they switch the question from enjoying mathematics to being good at mathematics. This might seem like a subtlety that no one cares about, but that’s not true. The difference here matters in an important way, because it affects how we perceive mathematics in general.

Do you enjoy music? Most people enjoy some kind of music, whether it is purely instrumental, pop, classic, rock, country, or the million other kinds of music. There’s something for everyone within the world of music. Furthermore, people tend to like specific kinds of music. They won’t listen to anything at random. They have taste in what they listen to.

I think it’s safe to say that most people aren’t any good at playing music. Most people aren’t musicians of any kind, yet they still listen to music! Despite the fact that they aren’t good at creating music, this doesn’t stop them from enjoying it. The act of creating music and consuming are distinct.

Likewise, you can find examples of this everywhere. People watch films, read books, go to sports games, consume fancy food, and look at art without being capable to create or do any of these themselves. If you ask people how they can enjoy these things without being good at it themselves, they will likely look at you in confusion. Who cares if I’m not good at these things? That doesn’t stop me from enjoying them.

Yet, we don’t seem to want to extend this mindset to mathematics. If we want to enjoy mathematics, the implication is that we need to be good at it. This is complete nonsense. Just like other cultural activities in our society, it’s possible to enjoy mathematics without being “good” yourself. You don’t need to have years of experience in analysis, algebra, and probability in order to learn something new and see the beauty of mathematics. Having that background may enhance the experience, but it isn’t a necessity.

“But wait,” you might protest. “Surely you need to be capable of understanding the mathematics in order to follow an argument? That means you have to be at least somewhat competent!”

This does have some truth to it. If you can’t follow any of the arguments, then the essence of the mathematics will be lost on you. But this is the responsibility of those presenting the mathematics. It’s up to them to make sure people understanding. No matter what your level, there’s an explanation available to you. It might not be the full explanation, but that’s to be expected. If you want to have the full explanation, you need to do a bit more work.

I can only think of one reason why mathematics seems like something that can’t be enjoyed just for its own sake. It is because we are forced to do mathematics from a young age. We are never told that mathematics is something we can enjoy. Instead, we’re told that we need to study these rules in order to do good on the tests. I’m reminded of the classic essay by Paul Lockhart, where he writes about how the educational system has ruined mathematics. He makes a lot of valid points, and the truth is that mathematics remains confined to schoolwork for a lot of students. The two seem to be inseparable.

In the first panel, mathematics is almost completely a subset of school, while the second shows it being only a small sliver. Impression versus reality.

This is unacceptable, and it’s something that needs to change. Mathematics shouldn’t be relegated to being seen only in school, because it has distorted the view on the subject. If you ask anyone about their experience with mathematics, there answer will tend to be linked to their experience with mathematics in school. This is a problem, because a lot of the curriculum doesn’t inspire wonder in students (at least, in the way it’s presented). The result is that students leave their mathematics classes with a bad taste in their mouths, and that’s what they remember. Rarely do students find enjoyment in mathematics. Wouldn’t it be great if we could reverse this tendency?

It’s going to take a lot of work to change the mindset of society at large. In general, mathematics is not associated with enjoyment and the reason given tends to be that a person can’t enjoy mathematics if they aren’t good at it. This is a perception issue. Everyone can find enjoyment in mathematics, it’s just a matter of finding the right explanation and topic. Like art, everyone has their own taste. If you read a book and didn’t like it, would you renounce your love of books? Of course not. You would turn around and try a different book. This is the same attitude we need to instill in people with respect to mathematics.

In particular, we need to encourage this behaviour in students, because they are most prone to fall into this trap. Since the curriculum is fixed, students don’t get to “opt out” of mathematics that they don’t enjoy. They have to grind through it, even if it’s boring to them. As such, we need to encourage students to go beyond the curriculum and to seek mathematics that excites them. Yes, mathematics can and should be exciting. However, not all mathematics will be equally exciting, and we need to be honest about that. Instead of making students feel like mathematics isn’t for them because they aren’t good at a certain part of it, we need to show them all of the other topics they can explore.

Mathematics is part of our culture, too. Encouraging people to get more excited about mathematics should be a top concern, and it’s one that I will be thinking about a lot more in the future.

Note: I got the idea for this post from a wonderful graphic illustration by a fellow mathematics blog which discusses an interview with the mathematician Eugenia Cheng. Go check it out.