Reimagining Mathematics: Professor Catherine Buell’s Keynote at MassURC 2025

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Professor Catherine Buell (left) and Dean Mari Castañeda (right). Photo: Eva Trainer

Dean Mari Castañeda opened the 2025 Massachusetts Undergraduate Research Conference (MassURC) Keynote by welcoming attendees from across the Commonwealth to UMass Amherst. She then invited Chancellor Javier Reyes to speak, who echoed the warm welcome and celebrated the outstanding undergraduate research being showcased. Encouraging students to stay curious and persistent, he offered the empowering advice: “Keep going. Keep the drive.” He then introduced the keynote speaker, Professor Catherine Buell, professor of mathematics and honors program director at Fitchburg State University.

Buell began her talk by sharing her goals: to introduce engaging mathematics scholarship, and to offer the advice she would give to her undergraduate self. Humorously, she showed a slide of all the undergraduate research she had undertaken—which was blank. Still, she emphasized that academic journeys can begin in many ways, like hers, which included a stint teaching in Springfield, MA.

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Photo: Matthew Medeiros

She then presented the research she has conducted—some related to her PhD and some not. One of the first projects she undertook in graduate school involved Frobenius pseudoprimes. She took the unprecedented step of emailing a researcher—a move she encourages every student to make—and he helped her understand the complex concept.

She also worked on visual stylometry and the digital humanities—a project that began from a casual conversation at a barbecue. In addition, she explored topics like history, dance, and art installations, which she says bring her joy.

Buell then discussed the area of mathematics she is most passionate about: tropical mathematics. This field involves a radical rethinking of basic operations like addition, subtraction, and multiplication. She explained the various oddities and intricacies of this mathematical approach, as well as the research she has conducted in the field with undergraduate students.

One student used tropical mathematics to optimize an assembly line, while another applied a Tetris-like mechanism to solve a research question—similar to techniques used by rail map designers.

Buell went on to discuss how she has branched beyond her primary field, sharing another of her passions: ethics and social justice in mathematics.

“Mathematicians have no code of ethics… Mathematics is not neutral, and mathematics was never neutral. Math as a subject area is a reflection of the values of society."

She gave examples of how mathematics has been used in harmful ways, including a real math textbook from Nazi Germany—an instance she emphasized was not a neutral application of math. Her current scholarship focuses on raising awareness of these pressing issues within the discipline.

Photo: Grace Chai

Inspired by one of her mentors, Buell now teaches in correctional facilities. In her course, she not only covers foundational statistical concepts but also incorporates topics of social justice—such as stop-and-frisk policies, mass incarceration, and gerrymandering—all of which can be explored and visualized through statistics.

In closing, she encouraged students to incorporate their personal passions into their research—just as she has done by integrating social justice into her work in mathematics.

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Audience members were invited to ask questions during the Q&A portion of the keynote. Photo: Eva Trainer

During the question and answer session, Shayna, an attendee from Worcester State University, asked for advice for students considering graduate education. Buell encouraged students to reflect on their values and seek out programs with cooperative rather than competitive structures. 

Dean Castañeda then asked why she is passionate about mathematics. Buell shared that her love for problem-solving and creativity began in childhood, sparked by playing board games like Rummikub.

Nicholas, another attendee from Worcester State, asked how she became involved in correctional facility education. Buell credited an incredible program at Mount Wachusett Community College and encouraged students to seek out similar opportunities.

After the program, Buell shared her hopes for the future of research and for what students would take away from the conference:

“This conference gives me so much hope for the future! I'm hoping that as folks go around, they’ll think differently about the research they see—and maybe they’ll be able to see themselves in those projects.”