Note: the above image was entirely created using math. Neural networks are awesome!
If you’re like me, you’ve always struggled with math. Elementary school, high school, college — when it was time for math class, I always felt like curling up into a ball and dying.
Most people, myself included, think math is just hard. That it’s intrinsically more difficult than other subjects, and math proficiency is reserved only the brightest and geekiest among us. I thought this way too, until my last year of university.
Story time: I’ve always excelled at school. I took Behavioral Neuroscience, a historically difficult subject, and crushed it consistently for four years with an A average. Physics, chemistry, anatomy, physiology — these were all a total breeze, so I always figured I was smart and capable. Until my last year, where my academic adviser told me I needed to take a first year math class to graduate.
I already felt the panic coming on. I hated math, and had done everything in my power to avoid it like the plague for the last half-decade. How could it have caught up to me?! In hindsight… that’s probably why I was in this position to begin with. I didn’t see the irony at the time.
Eventually, I de-curled from my ball of death and enrolled, figuring that things were different this time around — that I was a wise, intelligent senior and a class like this was only scary if you were a pimply-faced eighteen year old.
Right. Math destroyed me. Again. I studied night and day to no avail, and I barely made it through with a C, which was the minimum grade required to stay in my program. The worst part was, that single math class cost me my Honors designation, which, to me, was practically the foundation of my life at the time.
Immediately after receiving my grades, I was stunned. How could I have done so poorly? It’s clear I was a strong student from my other courses, so why was I so terrible at math? Was I just dumb? These thoughts and more were going through my head when, all of a sudden, I had probably my first truly great idea in five years: why not ask the pimply-faced eighteen year olds who walked out of there with an A?
So I asked them. And their answers floored me.
Almost every single student I spoke to told me something like this:
“I never read the textbook, dude. Those old textbooks blow. I just use the internet.”
To a student that was (at the time) treating every one of their textbooks like the Bible, this was news. Until this point, I had always thought that the best resource for acing a class was going to be supplied by the class itself. It just made logical sense — exam material was based off readings, which was based off a textbook… right?
Wrong. Immediately after graduating, I set myself on a path of self-discovery. I wanted to get to the root of why I sucked as much as I did, so I made it a point to spend time nearly every night developing my understanding of mathematics. I’ve now learned more math outside of a classroom than in one.
What I’ve discovered over the last year of study is that math is different. Math isn’t a bunch of disparate facts you need to memorize, like in anatomy or physiology. Nor is it a series of equations you need to regurgitate, like in chemistry or physics.
Math is a way of thinking.
It’s a way of approaching problems. Of conceptualizing the relationships between numbers, and understanding why things change rather than just that they change.
Math is not necessarily about being smart (though smarter people do tend to be better at it). It’s about looking at every problem from the bottom-up — without presuppositions and without preconceptions. And as you work on solving each problem, you get to build your understanding of the universe anew.
School tries to teach it to you from the top-down. You learn the formula, then you learn how to apply it, but you never learn why it exists in the first place. Derivations are rote-memorized, not understood. This is critical to developing an appreciation for the beauty of mathematics, but most of the time, academia ignores it entirely.
I struggled with math because I always took the word of my heavily dated textbooks as gospel. But that gospel was leading me astray. It’s not enough to treat mathematical concepts as mere facts to memorize — you must internalize their reason for being, and the necessity that spurred their discovery.
School will never teach you this. Not because they’re evil, or because they don’t want you to succeed, but because learning mathematics this way is simply not economical at scale. Public education would rather cater to the lowest common denominator than uplift a choice few, and that’s understandable given their responsibility to society.
If you truly want to learn this, then you must go outside academia. My journey to becoming smarter in math has included the following resources in order (some of these have changed not just my math skills, but my life):
- Math: Better Explained
- God Created The Integers
- A Mathematician’s Apology
- Journey Through Genius
- Calculus, by Strang (the first Calculus book I understood)
A note: you will not become a mathematical genius reading these books. If that is your goal, once you finish Calculus by Strang you will inevitably have to dive into denser and less readily-understandable material. But even if you finish the books on this list and no others, you will leave math with a deep and solid understanding of fundamental mathematical principles — principles which the vast majority of people will never understand in their entire lives.
A note — reading these books in succession and truly understanding them will likely take some time. Personally, it took me close to nine months. I spent only twenty minutes per night on average, but they were often the best twenty minutes of my day. Being able to retreat into a cozy nook in my room and fill my brain with beautiful numbers is now one of my favorite things to do.
Mathematics isn’t easy, but it is possible to understand. We were simply misguided on how to get there. You don’t start from the top-down — you start from the bottom-up, and build your understanding line by line, page by page.
If you found this article helpful, I encourage you to clap and share! More people need to revel in the beauty that is mathematics, and articles like this are one way to spread the word!