Entry #1: Mathematics (For Fun)

 Background

At the moment, I have several math textbooks saved in .pdf format and, on my bookshelf, I have two physical textbooks by Richard Courant. My GPA in high school was awful, and I read mostly texts on philosophy or history when given the time. You might want to know how and why someone like myself would bother doing math in my freetime; better yet, you might be interested in how this could even be a hobby.

To make matters more complicated, I'm actually taking two math courses at once during this semester. This isn't out of particular interest, but in fact to keep up with the requirements of my degree - I'm pursuing computer science with the goal of trying out a math major in the future. The classes in question are Calculus II and Discrete Math Structures, coming from two different "types" of math, to put it generally. I'm not picking up the content any faster than I'd expect to, and the work is doable but not easy. I don't actually have any inherent math ability, nor am I any type of genius. The last class I took in high school for math was precalculus; I would've finished with calculus, but I spent all my "study time" that I was supposed to use to get ahead to listen to music and finish homework due for the next class period.

[Source: Jeswin Thomas]

Who am I? What type of person am I?

I hate relying on memory to get something done. I don't bother thinking about my intelligence or an IQ score. To learn something, it's a lot easier for me to read, very slowly, sometimes spending a whole 30 minutes, or even an hour, on a single page. For school, I use the work as a means to get the general idea of a topic. In my freetime, I work a completely different way.

This is the root of using something like math as a hobby.

Sometimes I watch math videos in the same way that someone would watch a video for entertainment. I've heard of math like an art, and I agree. You don't need to know how to paint to look at a painting by Vincent van Gogh. In addition, if you've never painted before you don't need to understand everything in a matter of days for the sake of learning.

But, when it comes to trying something as a hobby, at least in the way that I think of hobbies, there is usually a learning curve where you may need to hit one or two plateaus before gaining new insights and going further. This is yet another point in favor of using something like math as a hobby. Through elementary school, middle school, and high school, I was already given the skills for arithmetic, basic algebra, trigonometry, and geometry. For most people, this is attainable, but I'd make the claim that it's insufficient for my needs.

Where's the Fun in Math?

After high school, I tried watching some videos on calculus and kept finding that people were struggling with the algebra and trigonometry that they supposedly learned in high school. I couldn't figure out how it was possible, until I tried evaluating some limits and derivatives. I didn't know a single "trig identity". I had no idea what partial fractions were. I did, however, recognize the process of using the difference quotient, but I had no idea why it was called that and had no memory of ever using that term to describe it.

Something was wrong.

I explored some YouTube channels, and ended up finding a video by The Math Sorcerer on self-teaching math. Keep in mind that I was not enrolled in college at the time, but I did of course later take a Calculus I class. Until watching videos like these, I thought calculus was one of the last math classes anyone would have to take. Upon the recommendations, I tried out a book for college algebra, followed by a book typically taught for high school and college students in precalculus, followed by a couple of chapters of a book in discrete math. Yes, I worked through dozens of discrete math problems some years before even taking the class for the first time this semester. It was totally different. The issue, however, was not learning the math: it was learning the techniques of problem solving. I found ways to push myself through messing up a problem terribly and struggling to finish certain difficult problems that I sometimes didn't resolve for an entire week, as bad as it sounds. After pulling through and getting the basics back together, I even opted for looking at a copy of a book called "How to Prove It". In this book, I ended up at several points where a problem looked impossible one day, then I'd wake up the next solving it in my head and walking straight to my notebook - first thing in the morning - with the problem out, solving it perfectly.

The last thing I did before taking my first calculus class was going straight to a website with a mini-book called "Trig Without Tears", available on BrownMath.

[Source: Dan Cristian Pădureț]

This is where the fun of math comes.

This method of learning is very time consuming and removes a lot of reliance on memory, but having good memory turns this into a far easier experience. As you may recall from earlier, I don't like using memory, so you can imagine that this way has helped immensely on my journey of learning these concepts. When I reach a certain point, it doesn't intimidate me when I realize how little I know and it doesn't both me so much when I fail or miss several problems, no matter how easy others might find them. Sometimes there are even phases of overconfidence, however, and these also do not bother me. To me, a period of arrogance, followed by a period of struggling, followed by a period of stagnation, and followed by a vague feeling of "unknowing" are all natural pieces of the advancement of learning. It's like a cycle to me, and I feel that I can apply this to my life more generally. I think I'm too young to glue my brain to thinking in only way particular way, and I don't want to ever feel like I'm "old enough" to stop the process.

"But, I Hate Math so Much"

... is a common saying I hear and see everywhere I go. Why is this the case?

Aside from dyscalculia and severe cases of math phobia/anxiety, there are still prevailing ideas behind the negative image of mathematics that have a real effect on people who purely take these classes for general education.

This might come as a surprise, but I have the same problem with art. I don't think I ever cleanly passed an art class, without pulling through last minute to do the bare minimum. Since the earliest years of school, art class has made me extremely anxious, uncomfortable, stressed, and spiteful. Yet, I really love the arts and can respect a good artist.

In my opinion, this is a natural response. Afterall, math is hard, and it's not always easy to make a good piece of art either.

Finishing Remarks

I think one thing, if anything, that should be the main takeaway for me presenting one of my hobbies is to try looking at math the way I look at art. I could learn how to draw and I hate taking formal art classes, but regardless of skill I can still enjoy a nice piece of artwork.

As a suggestion, I'd ask that anyone holding a certain negative view of math watch a YouTube channel like 3Blue1Brown or Numberphile, to pick up on the beauty of math as an artform. Always remember that everyone reaches a point where they struggle in math. There is no shame in reviewing content that you were supposed to know from earlier. Some people got stuck learning about fractions, while others don't get stuck until they start their first differential equation, and some don't even struggle until they go to grad school. If you lack the prerequisite knowledge, it is not an insult to ask of you to go back and review the material needed for present and future classes.

It's not worth letting yourself fail at high school algebra when you're learning college calculus, and it's unreasonable to expect yourself to perform at your best when you don't have all the gaps filled in to do so; you can't do what you haven't learned. Math is a subject that builds on everything before.

Most importantly to keep in mind: if you never "get" math as a school subject, you can always "get" math as a craft.