DiBeos

In the world of STEM, math has a really strong psychological weight. And it’s not just about the fact that math is hard in itself, but in many cases, we see math as a status symbol.

Most people come to the conclusion that being “good at math” is the same thing as being “smart”. So what happens when you’re usually very good at math, but one day you find yourself struggling, or even worse, failing, in a math-related area? Like you try and try and try, but, for example you can’t really understand what you are reading in an advanced math book. Or you can’t really grasp how to prove a theorem.

I remember when I was doing my master’s and I had to pass a class on Commutative Rings. To be honest, Abstract Algebra has never been my strongest area, but I do find it super interesting. Anyway, I remember I did really badly in the first exam, and the professor came up to me and said that I didn’t know anything about algebra and that this was my problem. He said he would not help me because I just didn’t have the correct foundations, so it was useless to try. I mean, he was right, but I took it the wrong way and even though I worked hard and passed the class, I feel like I never really learned the main concepts of commutative rings, like ideals, quotient rings, modules, etc. And I think it’s mostly out of an unconscious fear I have, based on this bad experience. Honestly, I found myself procrastinating many times to pick up a book on Commutative Rings to try again.

So the fear lies not in the fact that you may, and probably will, get stuck for hours while trying to solve a problem. But in the uncomfortable thought that this failure shows something deeper about you: that fundamentally, maybe you just aren’t smart enough.

But the thing is, in my opinion, this sense of exclusivity does more damage than good for mathematicians and for the general public that is interested in math.

Having a good reputation in general is an important thing in society. When it comes to academic circles, being really good in your field earns you a lot of respect. So if you’re able to work on a tough proof, or talk about abstract structures and casually use some fancy mathematical jargon, people are bound to look at you differently. And it feels nice. But what happens if you fail, like I did?

Failure happens to all of us, so, what if you can’t follow a lecture, or a book, on something like Commutative Rings, for example? The fear is not just that you lack what it takes to succeed, but also that you will be seen as an imposter. There’s a feeling of “maybe you’re not mathematically advanced enough to be part of this?”

Of course there’s also our internal lens. For someone whose identity is wrapped up in their intellectual abilities, especially when it comes to math, failing feels devastating. 

It’s not just “I didn’t understand this”. It becomes more like: “Am I not who I thought I was?” And this moment of doubt creates a lot of pain, because it might produce a sort of “identity crisis”. I don’t know if that makes sense to you or if you can relate, so if you do, or don’t, anyway leave your thoughts below. I’d be curious to read them.

There’s also the fact that in order to actually understand something in math you need to put in hours and hours of study time, and often follow a path that leads to a dead end. Which basically means you’ve wasted the last two hours. Or three. Or even your entire day with no results.

The thing is, people nowadays (and I include myself in it) are addicted to instant gratification, to get quick results. And when we don’t get them quickly we think: “If I didn’t understand this in one or two days, maybe it’s not worth it, or worse, maybe I’m not capable of getting it at all!”.

Some people have very low self-esteem when it comes to math. You can clearly see how this insecurity is blocking them from growing, even though they really enjoy the subject.

And the problem with this fear is that it leads to avoidance. People end up avoiding topics that challenge them, even if only at an unconscious level.

So my advice is to convince yourself that struggling is normal. Even really talented mathematicians spend a long time stuck on problems. The difference isn’t that they never fail, it’s that they’re willing to fail productively. They fail fast, so that they can learn quickly what are the ideas that will lead to dead ends, and this way they don’t take that route again. 

The truth is that the deeper you go into mathematics, the more you’ll struggle, the more it will be obvious how much you don’t know, but the rewards are much greater too, and that’s a good thing.