This summer, Mathematics Chair Kim Spayd and four Gettysburg College students took a mathematical approach to studying romantic love through the lens of addiction. Thanks to a National Research Experience for Undergraduates Program (NREUP) grant from the Mathematical Association of America (MAA), Spayd has been able to collaborate with her students to engage in applied math research while exploring a novel topic through mathematical modeling.
In preparation for this work, Spayd pursued her scholarly curiosity during her fall 2023 sabbatical. She sought to model the brain’s biochemistry during the early stages of romantic love. Through preliminary research, Spayd said she discovered “a lot of connections (implicit and explicit) between the way the brain responds to exposure to a beloved and the way the brain responds to an addictive stimulant like nicotine or cocaine.”
While her research uncovered substantial work from biochemists and psychologists on romantic love—and much from mathematical research modeling different types of addiction—“there was no mathematical approach to romantic love through the lens of addiction that I found,” she added. “With all the open questions available, I realized it was a perfect opportunity to involve students. They could make meaningful, original contributions and gain practical skills that will serve them well here and beyond.”
For eight weeks this summer, Spayd and her students, biology and mathematics double major August Butcher ’26, mathematics major and music minor Liz Callan ’26, mathematics and Spanish double major Andrew Lopez ’25, and mathematics and East Asian studies major Sophie Nasir ’25, focused on creating and analyzing mathematical models of the brain during the early stages of romantic love. Spayd and her student research team considered dopamine production specifically, given its prevalence in addiction literature.
“We started with a lot of background reading to understand the biochemistry and state of the current conversations in the addiction and romantic love literature,” Spayd explained. “Then we looked at simple mathematical models that use ordinary differential equations to describe how dopamine is released in the brain under different addictive scenarios.”
Analyzing the models allowed Spayd and her students to draw conclusions about the elements suited to a romantic love application. Her students furthered their research into learning and reward models, adding context to their dopamine inquiry.
“In the end, we came up with a system of differential equations that qualitatively captures dopamine and orexin—a neuropeptide that precedes dopamine release—production in the brain on short and long timescales,” Spayd said.
At Gettysburg College, student-faculty research opportunities like this one enable Gettysburg students to apply their breadth and depth of knowledge and development of enduring skills through the Gettysburg Approach to high-impact experiential learning, such as applied math research.
“There are so many open questions that have accessible entry points and that benefit from multiple perspectives,” Spayd said. “With the summer research on romantic love, we made great progress by sharing our various areas of expertise—mathematics, biology, chemistry, psychology, and programming—and building off one another’s ideas. I enjoy teaching at Gettysburg because faculty and students are able to connect in this creative, impactful way.”
The MAA supports undergraduate engagement in mathematical sciences by providing undergraduate students with focused, intensive research experiences. The NREUP provides grants to mathematical sciences faculty to create summer research programs at institutions like Gettysburg College. Through the NREUP, the MAA strives to increase undergraduate completion rates and encourage students to consider graduate studies by engaging them in research after their sophomore year.
By Michael Vyskocil
Photos provided by Liz Callan ’26, Jason Minick, Shawna Sherrell, and Kim Spayd
Posted: 08/06/24