A week before my AP Calculus exam, I realized that I probably should start studying. I whipped out my unopened Barron’s Prep Book, hopped into the first diagnostic test, reviewed what I got wrong, and then I put it away. This time would be different.
Up until this point, I was the one to talk about how the school system was apt to reward memorization over understanding. But, this time, I was going to stop playing their game. I was going to learn math the way it was supposed to be learned: by building up from first principles.
When a friend recommended 3Blue1Brown’s “Essence of Calculus” series a few weeks before the exam, I was a bit skeptical. I had an exam coming up — I didn’t have time to watch four hours of videos that would just repeat what I had already learned. I had to do practice tests. Active recall was king!
I turned to active recall during my first psychology test. Discovering Ali Abdaal’s study series on YouTube, I changed everything about how I studied. I switched out rereading for testing myself. And I no longer took notes but rather asked questions I could input into a flashcard system. I dedicated myself to this new strategy, and it worked. I got great grades. I don’t remember much from that class, though.
It happened again when I was prepping for a neuroscience trivia competition during COVID. Everything was made into a flashcard, and I was on fire with those questions. I don’t remember much from that topic either.
Humans are obsessed with measurement. It doesn’t take many years of state standardized exams to realize that the worth of a school is boiled down to a number. I’m one to talk, though: I am majoring in data science for heaven’s sake. It’s hard to measure understanding but easy to measure memorization. In Ultralearning, Scott Young offers the example of knowing the capital of a country. Whether you know or not is inherently binary. But, understanding calculus? Not so easy to measure.
The school system has rooted memorization to the core of what it means to be educated. If your success is determined by test scores, and test scores largely reflect how well one memorized concepts, you are rewarded for regurgitating information over understanding how that information was obtained.
Science is not the study of the known, yet we teach it like it is. The entrepreneurs, researchers, and innovators that changed the world stood at the edge of chaos, pushing the limits of the known and finding solutions to problems yet to be solved.
It was when I started watching those Essence of Calculus series that things began to click — that I began to saw the beauty mathematicians kept talking about. I built from the ground up, using my first principles to unveil the hidden secrets of mathematics. Could I have just remembered formulas for each problem? Yes. But, I preferred the real way of doing math: returning to your understanding of first principles to better understand the world.
I started to comprehend Naval Ravikant’s suggestion that if you are reading a good book, you should read a page and then think about that singular page for a while. After practicing this a few times, I think I know where he’s coming from. When I take a step away from reading what the author wrote and try to piece it apart on my own, doors begin to open and light shines down from the heavens. I achieve a state of understanding that I don’t get by simply reading page after page.
Maybe one day, schools will move away from memorization. But until then, I’ll keep carving my own path, looking to first principles to find truth.
