Jeremy Côté

Mathematics Isn't Just Numbers

We often equate mathematics with numbers, as if mathematics doesn’t extend further than doing arithmetic. Each time this happens, I have to restrain myself from going on a rant. I want to grab the person by the collar and exclaim, “There’s so much more to mathematics than just numbers! It’s like saying that running is just a bunch of one-legged hops. While that might be technically true, it’s not the way most people would describe their experience. In the same way, mathematics is way larger than just numbers.”

Even within my own family, some of them still see mathematics as essentially just a bunch of numbers with the associated arithmetic. I’m in a mathematics program, and this still isn’t clear to them. I think that’s clearly a failure on my part to share the diverse aspects of mathematics.

I encounter (and recognize) mathematics everywhere in my life. I know that it’s responsible for a lot of what I see on the web in terms of illustrations and graphics, algorithms rule our lives both online and offline, and mathematics is present in all the engineering I see. Most of these examples aren’t purely about numbers. Sure, it’s difficult to get away from numbers in mathematics, but they aren’t always the primary players. And yes, you can find plenty of examples of mathematics in the “real world” which aren’t cringe-inducing (like you might see in textbooks).

As a mathematics student, I’ve learned so much that doesn’t directly involve numbers. I’ve learned a bunch of geometry, analysis, probability and statistics, abstract algebra, discrete mathematics, and graph theory. While numbers are present in each of these topics, they only serve to make the concepts easier to handle.

If I wanted to draw “mathematics” and “numbers” as two sets, the former would encompass the latter. In other words, numbers are a part of mathematics, but they aren’t everything. This is something that I want to make more clear to a general audience. Mathematics isn’t all about numbers. In particular, if you just look at the area of geometry, there is so much you can learn without even worrying about numbers. This is an especially fertile ground for those with a passing interest in mathematics.

The lesson is simple: there’s a lot more to mathematics than numbers. Of course, numbers are present almost everywhere in mathematics, but they aren’t the point in and of themselves (unless you’re studying number theory, perhaps). Mathematics is a lot richer than that, so there’s no reason to put it off if you’ve “never been good with numbers”.