March 6, 2020 | Feature

# patterns of the world

## math, art, and everyday life

article by Nicole Fegan, illustrated by nina yuchi

“My life seemed to be a series of events and accidents. Yet when I look back I see a pattern.” – Benoît B. Mandelbrot, mathematician, namesake of the Mandelbrot set, my favorite fractal.

***

Some days, I wish I’d been a math major. I sincerely thought I’d end up as one, too. I was going to be a topologist, or find a way to specialize in fractals, or maybe just become a professor. Waltzing into MATH0350 (Honors Calculus) as a bright-eyed, bushy-tailed freshman, I was fairly certain this was merely my first class in a long journey toward a concentration in pure mathematics. What they don’t really tell you about MATH0350—and what, frankly, they *should* tell you—is that if you don’t have prior experience with proofs or multivariable calculus, you are, for lack of a better word, *fucked*. And I? I was fucked. Within the first month, I experienced a shattering: Suddenly, everything about my future was called into question. I decided that a girl who cries happy tears about getting a C in an introductory math class—because *at least I didn’t fail*—couldn’t possibly be a math major. I couldn’t continue to call myself “a math person.” So, what next?

Before taking that class, I’d thought I had a good grasp on why I loved mathematics. Like most people, throughout elementary and middle school, I simply enjoyed what I was naturally best at. I wasn’t great at learning Spanish, but math classes seemed to take root in my brain. I was a lover of puzzles, I liked knowing there was a correct answer at the end of my hard work, and I found the mathematical process relatively pain-free. Listicles on websites like piday.org and topnotchteaching.com note all of these as “Reasons why math is important in life” or “Tremendous reasons to love math.” According to these sites, math is “helpful,” it’s “satisfying,” it’s “fun,” and, my personal favorite, it “helps out in the kitchen.” To be a lover of math is to be pragmatic about what skills will be useful later in life, or so some people say.

As high school dawned, math began to acquire for me a deeper purpose. Life felt chaotic and I needed something to stabilize the entropy. The solution, I found, was math homework. Sitting down with a trigonometry or calculus worksheet was a completely self-contained activity; I was (and still am) distractible, but math represented the perfect harmony of engaging and difficult, allowing me to get lost inside of it. English and history were inherently *human *subjects; in order to do well, you had to understand how the complexity of people and society function. Math, however, enabled me to use my entire brain without ever needing to think outside the scope of the problem at hand. Not only did my personal issues cease to exist, but so did the outside world. For a brief moment, it was just me and a formula, or me and a pattern to dissect, or me and a problem that I just couldn’t seem to solve until, finally, it clicked.

Math became an escape from the real world as opposed to a worthwhile interaction with it. And I’m not talking light escapism—I’m talking a desire for an insulated world so intense that by the time I got to college, the sheer notion of “*applied* mathematics” seemed borderline gross to me. The only math I considered personally worthwhile was that which existed for its own sake: math for the sake of further math, without any need to apply it in realistic settings. Why take a perfect thing and make it imperfect by adding, of all things, this vastly imperfect world back into the equation? Math alone was the world I knew, and it was the world I wanted to live in.

***

During high school, I found myself creating what can best be described as math art. Restless while sitting in class, I doodled in the margins of my notes, and, time after time, these drawings ended up bearing mathematical significance. A cute little proof of the Pythagorean theorem became my drawing of choice, always occupying space in the corners of a page when my mind got bored. I learned to recreate the curves of a circle using only straight lines. I drew black and white scribbles, filling in negative space to see how the shapes changed. I couldn’t do perfect math with my hand, but the inaccuracy added to the experience. My straight lines were never quite so straight: In a way, I was making new math and new art every time I doodled.

More importantly, I became immersed in writing math poems. For four summers in a row, I made it my mission to inundate my friends at writing camp with my unique adoration of math, its shapes, and the unexpected ways it crops up in our lives. I wrote love poems and elegies alike using math as my anchor, and in doing so realized that mathematics could be just as creative as poetry—interpretive, ubiquitous, and beautiful. After performing these poems onstage, my friends told me they had never loved math as much as they did then, and that they may not *really* get the theory of the fifth dimension, but they intuitively understood the feeling of it.

Something was going on there, something I knew I needed to crack. And, by the time I had nearly failed multivariable calculus freshman fall and resolved never to take a math class again, all I was left with were the poems, the intricate doodles, and a wide-open schedule.

***

As time has passed, I have moved further and further away from math in its traditional sense. In the wake of my unfortunate calculus experience, I dove headfirst into a double concentration in English and philosophy. The time I had previously spent poring over mathematical doodles was occupied by listening to new albums and watching movies that had passed me by for years. My interest in math—its problem sets, its formulas, its rules—was waning, but I continued to consider myself “a math person.” The intangible *something* beyond the mechanics of actually learning and doing math was what stuck with me. Whatever that *something* is, it has continued to govern how I view the world.

I wasn’t alone in believing that there is more to math than just its logistics. Outside the realm of vague listicles, people’s reasoning behind their love for math seems significantly more nuanced than “math can save you money!” Applied math concentrator Jordan Hartzell ’21 said, “Sometimes thinking about math feels like thinking about art; you have this set of materials that you can use to build up something that exists in the world or in your head.” In a 2017 Odyssey article, Kiki Shelly Ray discusses her personal reasons for loving math. She writes, “Math is an incredible thing and is both a tool for us to explain the universe and give it a language, as well as a beautiful art form in itself.”

I cracked the code when Gertrude Stein entered my life this semester in a class dedicated to her work. Stein’s work suggests she didn’t care too much for math, at least from what I can tell. She cared about the natural world, people, and the objects we create, but I have yet to find in her work a love for shapes, numbers, or anything of the like. Yet I kept noticing mathematical concepts in her supposedly non-mathematical art. In her essay “Portraits and Repetition,” Stein critiques the concept of resemblance, positing that when we look at things, “any little movement any little expression was a resemblance.” Reading this, I recalled my doodles of tangent lines, creating the illusion of a circle but never a circle itself—merely a resemblance. In the same essay, Stein discusses the portraits she writes of other people, saying, “If they are themselves inside them what are they and what has it to do with what they do.” Stein has a way of making everything sound beautifully convoluted, but to me, her portraiture echoes the pattern-like nature of a fractal. A fractal is a geometric figure of which each individual part has the same characteristic of the whole, forming a pattern that repeats into infinity. I believe Stein’s portraits function similarly: She identifies the essence, the fundamental nature of a person, and replicates this essence in words. Her portraits are essentially composed of their subjects. Stein may not have written explicitly about math, but she was more of a mathematician than she gets credit for.

Stein’s poetry evokes such a strong sense of mathematical understanding because I’ve realized that, for me, math is at its best when it seeks to explore the world rather than escape from it. Math is, after all, humanity’s attempt to produce a kind of perfection that the universe already creates without us. Italian mathematician Leonardo Bonacci is often credited with the “discovery” of the Fibonacci sequence, but the sequence existed in the petals of a flower and spirals of a pineapple long before Bonacci was even born. My interest in mathematical concepts like fractals stems from the notion that maybe, just maybe, math can transcend the constraints of our understandable universe. Mandelbrot once said of the fractal named after him, “The most complex object in mathematics, the Mandelbrot set…is so complex as to be uncontrollable by mankind and describable as ‘chaos.’”

Yet, when I look at the Mandelbrot set, I see with my human eye not an infinity but simply a series of circles, bulbs, and coiled lines: It is, in its own right, a work of art. Just as I have found math in art, there is beauty to be found in math. If modern art has taught us anything, it’s that shapes can be considered artful, and if Gertrude Stein has taught me anything, it’s that mathematical concepts are hiding in our everyday lives and the artwork we consume. Through whichever mediums we choose, we’re all trying to make some kind of sense of everything around us—the curves of the sun, the precariousness of love, or the beauty of the particular blue at dusk.

***

Perhaps, at this point in my life, it’s unfair to say I’m interested in math for its own sake anymore. These days, I learn the most about math when I read a book of Maggie Nelson’s poetry or visit the Institute of Contemporary Art. The concept of outliers makes more sense when I can visualize one yellow book in a room of blue, and perpendicular lines come alive when I picture them as two people meeting briefly, never to encounter each other again. Through art, I am discovering the intricate way our lives are made of mathematical patterns, repeating again and again into infinity.