2017 AWM Essay Contest: Undergraduate Level Honorable Mention
By: Lily Jordan Massachusetts Institute of Technology (Mathematics) (Cambridge, Massachusetts)
Jo Ellis-Monaghan knows her details. She’s an expert in the efficient gutting and gilling of salmon: it takes her fifteen seconds to process one fish. She can determine the sex of a crab with a careful glance: a male’s underbelly flap is bell-shaped, while a female’s is semicircular. In her spare time, she makes intricate ceramic pots.
An unusual combination of skills? Certainly – but nothing screams “usual” about an Alaskan- bred mathematician who conducts her research from a Vermont liberal arts college, calls a Lake Champlain island home, and considers herself an artist as much as a scholar. Although both her day job as a professor at Saint Michael’s College and her artistic craft demand technical prowess and rigorous attention to minutiae, Ellis-Monaghan values the big picture when it comes to crafting her own life, and so she has foregone the traditional mathematician’s path in favor of one that affords a balance among family, math, and art.
As a child, Ellis-Monaghan disliked math. Given her competitive spirit, she became discouraged when her classmates were able to do algebra problems more quickly than she. The only part of math class that appealed to her was geometry, where the material came in visual form. And visual forms were her forte – when she wasn’t at work in the Ketchikan fish cannery, she could be found in the studio or the theater. In fact, she entered Bennington College as a dance and drama double major. There, she focused most of her time on what she describes as the “intensely subjective” studio art work, but she began to dabble in math courses to have “something straightforward and objective as a way to relax.”
Her undergraduate studies were, to say the least, nontraditional. Bennington had only one full mathematics professor, so all of Ellis-Monaghan’s math classes were taught by Rein van der
Linde, a Dutchman with a fondness for analysis. Depending on the semester, she had either one or zero classmates. One night, she stayed out late and didn’t awaken in time for her 8 A.M. class. The professor waited five minutes and then marched over to her dorm, his other student in tow, and banged on her door, shouting, “Vhere are you! Ve haf already the class started! Get up now!” Ellis-Monaghan could see her classmate over van der Linde’s shoulder cracking up.
“Never missed again,” she says with a laugh.
It wasn’t until halfway through her master’s in mathematics at the University of Vermont that Ellis-Monaghan began to appreciate math in the same way she appreciated her artistic endeavors. She’d never planned on graduate school – she applied only at the urging of her advisor, who recommended pursuing a master’s instead of waiting tables so she could get paid to sit all day rather than stand, leaving her with enough energy to paint afterwards. Yet soon, under the influence of UVM mathematicians like Dan Archdeacon, Jeff Dinitz, Dave Dummit, and Richard Foote, she began to love research mathematics because it put her in “the same head space” as painting.
“I realized that the math was no longer pointless memorization and redoing junk in the back of the book,” she says. “The mental process was exactly the kind of visualization and structure and creativity I so loved in my art. And the rest is history.”
Some history, indeed. Ellis-Monaghan went on to complete a Ph.D. with Jim Stasheff at the University of North Carolina and launch a career as a mathematics professor, leading research teams in algebraic combinatorics and graph theory. Her latest work concerns an ingenious method of applying graph theory, usually associated with computing and networks, to the problem of creating self-assembling DNA structures in the lab. Using graph-theoretic techniques for finding efficient paths among nodes, her work helps biologists synthesize DNA molecules that arrange themselves, and the process goes in reverse as well: origami-like DNA arrangements represent solutions to graph problems, leading to new mathematical results.
The idea came to Ellis-Monaghan when she attended a talk in which computational biologist Nataša Jonoska described a promising experimental result regarding DNA nanostructures. Facilitating this kind of crossover is key to Ellis-Monaghan’s work, but it’s a learned skill. “You need to be a good listener,” she says, “to get your mind wrapped around the ideas in in different areas and see down to the underlying structures where there might be unexpected connections.”
When she isn’t working on her latest paper, Ellis-Monaghan helps students wrap their own minds around tough ideas. At Saint Michael’s, she teaches courses from calculus to abstract algebra. Of her students, she says, “I want to share with them the wonderful things I have found, kind of like how you want to get birthday and Christmas presents for your kids.”
She also serves as an editor-in-chief of Problems, Resources, and Issues in Mathematics Undergraduate Studies (PRIMUS), a journal of ideas about college math teaching. Among the most important such ideas, in her view, is the balance between rigor and intuition. “Doesn’t matter how good you are at nailing down the technical details, if there isn’t something you can see well underlying it, what’s the point?” she explains. “And if you can see well, but can’t communicate, you are dead in the water.”
One thing is for sure: Ellis-Monaghan can see well. She’s recently taken up Byzantine iconography, the ancient religious tradition of creating Christian images that draw on an established body of symbolism to relate Biblical stories via a sort of visual code. Currently, she is working on an icon of Isaiah for her oldest son, Isaiah. For Ellis-Monaghan, iconography is a combination of art, math, and spirituality. Like a dense algebra text, an icon contains an abstract beauty that, to the trained observer, shines through a system of formalisms. In Ellis-Monaghan’s view, the differences between her hobby and her profession aren’t so important. What matters is the language that each discipline gives her to translate the wonders around her into structure and back again.
“The only difference,” she says, “is in the end, do I paint, or do I write theorems, in order to communicate what is in my head with the world.”
About the Student:
Lily Jordan is a sophomore math major at MIT who has also sold about a quarter of her soul to Silicon Valley by means of a computer science minor. Her areas of interest include combinatorics, artificial intelligence, algebra, and graph theory. She is very proud of having sat through all six hours of this year’s Putnam with minimal squirming. The ellipse is her favorite conic section, and hand-waving is her favorite form of exercise.