Image Credit: Seth Yoo, from Measurement, 2/24/22
Oddly enough, I think I’ve only recently begun to understand what math is really about. For about as long as I can remember, math has always been one of my favorite academic subjects. In fact, it’s pretty much been at the top since I was in elementary school. Learning different operations and mastering them was a process that reminded me of video games. With each world (unit), I’d be introduced to a new level (topic), and after the initial playthrough (explanation), I’d be tasked with honing my skills until I could clear the stage flawlessly. Like a machine, I’d crank through tons of problems of a similar variant until I was highly accustomed to the exercise I was tasked with. This mechanical repetition, although it might sound boring, was actually pretty enjoyable. In the same way you learn new things about a level in a game as you keep on attempting it, math was all about bashing through problems while searching for patterns and shortcuts. However, if you asked me why math is fun now, this aspect of it certainly wouldn’t be my first response.
When I came to Brunswick, one of the clubs I quickly decided to join was the math team. I was under the impression that I was fairly decent at math, so I thought it could be interesting to see what a math team would look like. I went in with my mechanical image of math, but I was completely thrown off by what I ended up seeing instead. Of course, there were still problems that were based heavily on calculations, but there were also problems whose solutions felt like magic. How could anyone ever think of trying that? Such questions flew through my head as I watched my peers dismantle and explain problems I barely understood with apparent ease. Whether I had realized it consciously or not, looking back, it’s clear to me that my first year on the math team put into question so much of what I perceived math to be. One distinct memory I have from this period was when Mr. Allwood used the word “beautiful'' to describe a topic in math he had studied while we were driving back to campus after a match. It was a simple comment in a casual conversation, and I’m not 100% certain if that was the exact wording or context; however, what I know for certain is that through a simple comment of that nature, the idea of math as something beautiful was implanted into my mind. In what way is math beautiful? No matter how hard I thought about it, I couldn’t figure out how math, which was all about bashing out problems, could truly be called beautiful. With this question lingering in the back of my mind, my sophomore year ended and I entered junior year. Throughout my junior year, I continued to try to see the beauty in math, both in class and in math team. By the end of the year, I was a stronger math student, but I still couldn’t say math was anything beautiful.
Strangely enough, it was actually over the summer where I think my perception of math changed the most. More specifically, it was sometime in the middle of July when this really began. While I was browsing through Youtube, I happened to click on a video from the channel 3Blue1Brown that explained a proof for why slicing a cone makes an ellipse. This video made a deep impression on me, and I was blown away both by the proof itself and the explanation of it. It was just really cool. In the video, a book called Measurement by Paul Lockhart was recommended, and it was also where Grant Sanderson (the person who runs 3Blue1Brown) had first seen the aforementioned proof. I became curious, and I ended up buying the book, which is a decision that I don’t regret in the slightest. As of right now, although I haven’t even finished half of the book, what I’ve read so far has been enough to give me a taste of math’s beauty.
Paul Lockhart’s Measurement is a book that, to me, strives to expose the more artistic and creative side of math that’s often neglected. More than a formal book about math, it feels like someone going on and on about something that they’re genuinely excited by. It also explains everything in a way that doesn’t require much knowledge about math. Most notation and concepts are explained from scratch. When you’re reading it, it can feel like a conversation at times, as Lockhart answers our questions and leaves us with new ones to think about. Lockhart himself refers to math as an art: “I’m going to assume that you love beautiful things and are curious to learn about them. The only things you will need on this journey are common sense and simple human curiosity. So relax. Art is to be enjoyed, and this is an art book.” It is important to note that even if everything is explained in simple terms, the concepts he describes still take thought and effort to understand. “Mathematical reality is an infinite jungle full of enchanting mysteries, but the jungle does not give up its secrets easily.” However, if you do decide to put in a bit of effort and thought while you read, there’s a lot to be gained. If you’re someone who sees math as something more mechanical, that’s just taught to be “useful” later on, I’d highly recommend this book. You might see a whole new side to math that you never even knew existed. Personally, I was exposed to a fun and vibrant world of challenging problems and elegant solutions. After years of trying to figure out if there was more to math, I finally saw a world within it that could absolutely be described as beautiful.