The “fun fourth class” is a coveted space in the Brown undergrad’s schedule. As high schoolers, we were forced to churn out a couple hundred words on the importance of the Open Curriculum. Whether or not you’re living out college as your high school self said you would, you’ve likely taken advantage of it at some point in your Brown career—probably through your “fun fourth class.” As a humanities concentrator, I am sick and tired of the bulk of my courses being relegated to the realm of the “fun fourth class.” I get it—the small class sizes, the more scenic locations, and the quirky titles on the syllabus all make my courses easier to romanticize than, say, ENGN0090 or CHEM0330. But I refuse to let this romanticization be a one-way street that only traverses from B&H toward the Lit Arts department building. I will literally enroll in a pure math class just to make my point. 

That’s right, you didn’t misread—this semester, I’m taking Introduction to Number Theory, or, as I prefer to call it, MATH0420. If you don’t believe me about the course code, look it up on C@B. As I took my first math exam in college last Wednesday, the middle schooler in me—that snot-nosed, immature devil on my shoulder—secretly hoped that I would score a 69 on the test. Can you imagine? A 69 on my MATH0420 exam? (I’m 20 years old.) 

But I digress. At first glance, number theory might not seem like the most relevant thing to this so-called “real world”—how does the study of numbers actually affect anything that matters? Finding the next largest prime number won’t decrease the line at the Ratty or make it sunny again. (Though, fun fact, it could actually win you a lot of money!) Despite number theory's applications in cryptography, I’m not here to expound upon its importance to the security systems that protect our credit cards. If you wanted to hear about that, you’d be on the second floor of Salomon every Monday, Wednesday, and Friday, sitting next to me in the back by the open window with a beautiful view of the green (peak daydreaming territory). I’d like to share with you my personal takeaways from MATH0420, the ones you won’t find in the textbook, or on the Canvas site or the syllabus. These silly musings are mine alone. 

First, I believe the limit (no pun intended) to what can be feasibly romanticized is much higher than we think. For example, “problem set” is a phrase that immediately strikes dread into the hearts of students all across campus. And I can see why—the problem sets I have done for the class have been time-consuming and often futile, akin to suddenly picking up a shovel and trying to dig to the center of the earth. But even this laborious weekly undertaking can be made fun—just last week I sat on the green, in my best sundress and sweater, with the beginnings of the spring sunshine beaming down on the cream-colored pages of A Friendly Introduction to Number Theory. As I aimlessly attempted to solve a system of congruences (a Sisyphean task for yours truly), I was struck by the beauty of time as we travel along the x-axis of life. One moment you’re a high schooler who just got into Brown—“I never have to take a math class again!”—and the next, before you know it, you’re voluntarily in a pure math class because why not? Would high school me even recognize that girl on the green—legs crossed confidently as she attempts a ridiculously hard problem set for no reason other than to expand the realm of what she knows? 

I’ve also learned that math has many applications outside the classroom—namely, it’s a great conversation starter for your friends when the dining hall chatter has reached a natural lull. Did you know there are infinitely many prime numbers? Did you know that there is no such thing as an odd perfect number—well, more specifically, we haven’t found one yet, so we don’t know if they exist? Additionally, the way we prove things in MATH0420—trying a bunch of examples, ascertaining a pattern, formulating a conjecture, proving the idea, repeating for every theorem in mathematics—has a beauty to it that I think we could all learn from. What if we all looked at what’s going on in our lives through the lens of an amateur S/NC mathematician? What patterns do you notice? What trends do you see? How do you feel about them? 

The thing about number theory is that it’s constantly changing—old conjectures are finally being proven centuries later, computers allow us to work with numbers larger than ever before, and bold, new, mostly incorrect claims are made by students at Brown University as they hastily finish scribbling their psets before the weekly deadline. If numbers—arguably older than civilization itself—and what we know about them are constantly changing, then why can’t you? So, pick up those knitting needles, cut off that toxic friend, audition for that show—it’s never too late. 

What strikes me most about number theory is its vastness. With an infinite amount of natural numbers, to prove anything that holds true for all numbers seems to me to be a pretty miraculous feat; you can always find me in awe in the back of the classroom after a particularly elegant proof has been drawn on the chalkboard for us 20 lucky students. At the risk of sounding like I have partaken in 4/20 rather than MATH0420, I believe life is similarly infinite and rife with potential, brimming with that electricity of the unknown, like how I imagine those huge primes that live outside the realm of the known ones. So what will you do with your vast, infinite life, a life that is filled with so much potential we could not possibly fit it on a Cartesian plane? 

The number one (“1” in mathematician speak) comes up a lot in number theory. Neither prime nor composite, the divisor of any whole number you could possibly come up with, 1 is the beginning (if we’re starting at 0 and neglecting those negatives) of something infinite. 1, with its sharp shoulders and beautiful square base, may not know that beyond it lurks an infinite sea of numbers that never ends, that not even the best computer could ever reach the end of because there simply is no last number. Just like our friend 1, you have one (1) mind, one (1) body, and one (1) lifetime. What will you do with it? I, personally, am going to learn about some numbers. 

QED.