Today, I want to talk about struggling with mathematics. I think the best way to do this is by reacting to something G.H. Hardy said.
While doing some research on Hardy, I came across a blog by Maria Popova of Brain Pickings. I was overjoyed to see one of my favorite writers talk about my favorite mathematician. In her writing, she tackles the ideas of what we make of talent and ambition.
She quotes a passage from A Mathematician’s Apology.
I am not suggesting that this is a defence which can be made by most people, since most people can do nothing at all well. But it is impregnable when it can be made without absurdity, as it can by a substantial minority: perhaps five or even ten percent of men can do something rather well. It is a tiny minority who can do something really well, and the number of men who can do two things well is negligible. If a man has any genuine talent he should be ready to make almost any sacrifice in order to cultivate it to the full.
I wonder though, is there worth in the endeavor to better yourself in the areas where you struggle? This reminds me of my own struggles with mathematics and why I’ve chosen this path. This is an area with which I disagree with Hardy’s advice. Although, it may not be the best path. It is the one that I have chosen to follow.
Why I Struggle with Mathematics
I don’t believe that I have a natural talent for math. If I do have talent, it is probably language. Not in terms of spelling or grammar. It is mostly in terms of vocabulary. In understanding the denotation and connotation of words. I write and communicate frequently in text (well my whole career in community management is communications work.) As well as an adept ability to learn foreign languages quickly.
I will admit that I have some intuition for math. It doesn’t come from a natural ability for numbers. In fact, at a very early age I struggled with number sense. Mainly, I could not understand the quantity. When I was learning multiplication, I would spend recess with my math teacher. She would try to help me using cubes. A single cube for ones, sticks of ten cubes, and rectangles of 100. She would ask me what 10 x 10 was. I would stare blankly at her. She would tell me it is 100 and I would count each individual cube to make sure it was so.
I now understand that problems like this are common with Dyscalculia.
I had many of the difficulties that the researcher in this video talks about. The most salient one for me, the analog clock. My parents never believed me when I told them I didn’t know how to read a clock. I still have a disdain for watches because of it. Something that put me at odds with my father who was a watch collector. It was not a love we shared.
The way that I learned math was treating it the same as language. I created a substitution code that traded numbers for letters. When the math was all in symbols, I could translate the meaning of the sentences. It is easier in my head to look at symbol like a and understand that it represents 7. If I see 7 in an addition problem then I’m counting each one in my head. I’m not surprised that my fondness for math comes in the form of equations. Give me some variables and I am good to go.
Struggling with Mathematics is my Preference
True storytime. For a while, I was a member of an online dating website. I was matched with a person and we started talking about the things we like. Of course, I started talking about mathematics. Which he chimed that I must be good at. I said, not really. He asked me this question, “Why would you choose to pursue something you are bad at? It would make more sense to follow your strengths.”
He is not wrong. Studies of self-improvement show that we overestimate our ability to make changes in our weak areas. We actually grow more by using and practicing our strengths.
The things is, I don’t get the same feeling working on writing as the feelings I have for mathematics. I write every day even when I don’t publish. It is just something that I do that I’ve always done.
With mathematics, every new insight feels rewarding. I feel there is a large deficit that I need to cross. It is like being adrift at sea with a compass. I keep following a course making small self-correction over time. Eventually, I will make it to the shore. I just don’t know when or where. Yet, I feel guided to do this work.
There is something to be said for developing natural talent and ability. How we choose to spend our time and energy should also be enjoyable. It is not worth doing something against your will because you are good at it. I think this is something missing from Hardy’s statement.
One of the most interesting passages to me in A Mathematician’s Apology is Hardy’s discussion of becoming a mathematician. He studied mathematics because as a child he could “beat the other boys at it.” He only considered himself a mathematician after reading Cours d’Analyse. I think this gives some background to the Hardy quote at the beginning of this article. Yes, he pursued his talent but he didn’t see it as his profession until he read that book. So I think it has to be more than talent that causes you to choose your path.
Is Struggling With Mathematics Worth It?
Now, I know what some of you might be thinking. That I must have more ability than I give myself credit. After all, I have successfully passed my math classes earning an A grade. You may not believe me when I talk about the effort to do so. So am I following Hardy’s advice by studying mathematics for a BA degree? Well, maybe yes and maybe no. I don’t know it if is a genuine talent. It is something that I love. You know, I just gotta give myself a chance.
Here is something most people who hate math don’t understand. Everyone struggles with mathematics. Period.
I know this is a hot take, but it is my own opinion. I think the reason why people think that you are a genius for studying math is that we only share stories about math geniuses. The every day mathematician doing their work may never become well known outside of their field. No matter their talent or ability, they have chosen a path to acquire very specific skills. They all started somewhere and struggled like you are now. Mathematics is too wide a subject for every mathematician to know or like every aspect of it.
We can take solace in that.
I think that what holds most people back from exploring mathematics is math anxiety. I still struggle with this myself. I went into one of my midterms this week and couldn’t solve half the problems. My professor allows for exam corrections. Doing these problems at home has shown me that I do understand them. I was able to complete most of them on my own with more time. I must have panicked. When you panic, you lose access to your working memory.
I think that if I can pass calculus that you can as well. You just might have to re-visit the parts of math that make you freak out. If you can make peace with that, you are well on your way to improving your mathematical skill. I know you can do it.
I recently read two great pieces about struggling with mathematics.
The first is from maths advocate Jo Boaler. She recently published an essay about why students should struggle with mathematics. That they improve more when we don’t immediately give them answers.
My math professor pointed out the other, “Living Proof.” It is stories from mathematician’s about their personal struggles. It is free to download. I think resources like these are very important. It shows the daily life of mathematicians.