Painting is an extremely applicable skill to learn. If you can paint, you'll almost certainly be able to get a job that pays a great hourly rate, you'll be able to help a lot of folks, and your services will always be in demand. With some basic managerial skills, you'd also be able to build a scalable business out of it.
I'm of course not talking about oil painting on a canvas, abstract water color painting, or any painting you'd see in a museum – I'm talking about painting houses (interior and exterior), fences, and decks.
I'd be willing to bet, though, that there was some confusion about the first paragraph because the picture that came to mind from the word "painting" was indeed the "museum kind" of painting – and that is certainly a terrible way to lock in a good hourly wage or build a scalable business. The lack of scalability and stability of a museum-type painting career is not a knock on that career, it's just not what that type of work is meant to optimize, and people typically know that.
When it comes to painting, we have a pretty clear understanding of how it works: there are types of painting that are "applicable" to modern society and the economy, and there are types that are not. We're okay with both types, and we typically view one as a job and one as an art-form (please don't take this as a knock on house painters – many of them are fantastically skilled as well). We, society, can hold both things in our heads at the same time, no problem.
Why, then, can't we do the same for math?
The Curse of Applicability in Math
Just like painting, there are types of math that are extremely applicable to the functioning of society and to the forwarding of one's career. And then there's math that's really not. For reasons we'll get into shortly, we as a society struggle massively to both understand that there's a difference at all, and even when we do, we struggle to keep both things in our heads at once and appreciate each for what it is.
The way I see it, there are two main reasons for this.
Reason 1: Math is SO applicable
Painting houses, decks, and fences solves some big problems for us. To name a few, all of the following issues are problems that painting can fix, a service for which we happily pay:
- ugly colors
- visible smudges
- water damage on wood
- rust
While these are important problems to solve, they pale in comparison to the problems that math can solve. To name a few:
- all forms of engineering problems
- all forms of accounting problems
- all scientific endeavors
- the literal functioning of all of modern society's technology stack
With math being able to do so much for us in virtually every facet of modern life, it's hard to even imagine that math could do more. Therefore, "math as an art form" is something that gets forgotten about – or really, ignored entirely.
Reason 2: Sometimes, even the inapplicable stuff becomes applicable
To make matters even worse – or just more confusing – sometimes the "artsy math" actually becomes wildly applicable at some point in time. Namely, despite what was discussed in the last section, some people still do turn their back to applications and go off doing math just for math's sake. They find all kinds of cool stuff that is, at the time, completely irrelevant for anything social or economic.
But then, sometimes 1, sometimes 10, sometimes 100 years later, a new problem arises whose solution lies in that "artsy" math. This happened a ton once computers hit the scene, but also long before that. People playing around with the very artsy question of whether or not Euclid's fifth postulate was really necessary, f***ed around and discovered non-Euclidean geometry. This became the necessary framework for Einstein's theory of gravity which now is the backbone of many of our most important modern technologies.
So, even when mathematicians try to do the artsy stuff, they sometimes accidentally do the other stuff. I don't think they're mad at the fame (and sometimes riches) that comes with that, but that's not why they did it. The "problem" with this, though, is that it makes people think that we should choose which "artsy" things to do based on the likelihood that it might one day cross over to the other side. And this just confuses the matter even more.
Is this a problem?
So far I haven't said much about why this is an unfortunate state of affairs – i.e., why it's a curse. Some people think that math should be applicable, others think it can be inapplicable as long as it might become applicable someday, and still others see it as an art form. That's fine.
The problem comes from the fact that we – not everyone, but society "in general" – struggle to keep all these perspectives in our heads at once. Namely, an oil painter doesn't need to justify what their painting is "used for." We know what it's used for: nothing. More specifically, it's fun to look at, it was (presumably) fun for the artist to make, and that's enough. In fact, that's more than enough. No one expects more from it.
When it comes to math, though, we expect it to be applicable. We then only teach the most applicable stuff – which is not always the most fun stuff – and often frown upon the artsy stuff. This implicitly discourages the kinds of playful, curiosity-driven exploration that is at the heart of mathematics.
It's important to note, too, that this division between applicable and artsy does not need to be on a per-person basis. Many people make a living doing applicable math and then come home and do the artsy stuff. If we can hold these different perspectives in our head simultaneously – the way that we do for painting – then we can see each for what it is, have more aligned expectations for each, and be clearer on what and how we teach future generations of mathematicians.