Using mathematics as a model for thinking
Erin Griffin teaches differential geometry, but she focuses on how learning mathematics can form community, confidence and clarity in communication.
Imagine a water balloon being held by a fishnet. Place the net on a table, and the grid of its netting hangs loosely around the balloon. Lift the net, and both the balloon’s shape and the grid surrounding it begin to change.
For Erin Griffin, assistant professor of mathematics at Mount Holyoke College, that image offers an accessible road into differential geometry, a field that uses tools from calculus to understand curved, higher-dimensional spaces.
“There’s a connection between the grid that we’re using and the shape that an object is taking on,” Griffin says. “The question that we’re trying to answer broadly is: What is the best grid? What is the best metric?” Another example, Griffin suggests, is that the grid of latitude and longitude that we use to pinpoint our location on the spherical Earth does not fit that sphere uniformly. Among other questions, differential geometers ask whether there’s another way to measure Earth’s surface that better fits its shape. More generally, answers to questions about shape contribute to scientists’ understanding of celestial phenomena, such as black holes.
Griffin was drawn to geometry because she enjoys thinking about how things look, move and change. She took geometry courses as an undergraduate at California Polytechnic State University, San Luis Obispo, and she began wondering whether she could study the subject professionally. A professor introduced her to differential geometry.
Griffin compares herself to a general contractor who needs to understand “a bit of plumbing, a bit of electric [and] a bit of carpentry.” Differential geometry draws on several fields of mathematics, letting her connect ideas rather than specialize narrowly in one, which suits her broad academic curiosity.
That curiosity also shapes her teaching. Griffin wants her classes to feel communal, where students know and support one another. Students are more likely to engage in class, attend office hours and persist through challenges when their classmates are allies in wrestling with challenging material.
Griffin believes studying mathematics is not just about knowing formulas and making calculations but also about learning to approach problems logically and explain solutions clearly. “How can we be good critical thinkers,” she asks, “who are thinking in a way that is logical, … repeatable and easily communicated to other people?”
Mount Holyoke appealed to Griffin because its liberal arts mission reflects how she approached her own education. Although she majored in mathematics, she minored in philosophy and studied music and religious studies. She was also drawn to the College’s identity as a gender-diverse women’s college. As a woman in mathematics, Griffin remembers how important it was to have teachers recognize and encourage her, and she looks forward to offering that support to Mount Holyoke students.
Outside the classroom, Griffin engages in activities that she is new at and can make progress in. “Getting good at something unfortunately requires being bad at something,” she says. Her current pursuits include rock climbing, boxing, golf, sewing, baking sourdough bread and learning to build or repair things. A former college lacrosse player, Griffin also likes long walks with her wife and their dog Ricci, who is named for a mathematician. Their cat Hubble enjoys watching Survivor with them.
