Daniel Lee ’26 approached his thesis with a specific goal: to find a problem rooted in topology that also had a computational dimension to it. A math major from Taipei, Lee was enthralled by the elegance of topological thinking he encountered in his courses at Haverford, but he really believed his future was in applied and computational math. The thesis, he decided, would have equal footing in both realms.
His work led him to the J. McLain King 1928 Professor in Mathematics Joshua Sabloff, whose research focuses on many facets of topology, which focuses on geometric shapes that remain unchanged despite deformations such as stretching or bending. Sabloff shared a paper with Lee that explored whether machine learning and computational techniques could shed light on an open problem in the field, then suggested that Lee investigate whether those methods might apply to a related, less-studied area. After reading the paper, Lee says he was immediately on board.
The result is “Computational Methods for Identifying Knots Bounding Möbius Bands,” through which Lee explores how knots in three-dimensional space behave when they are bound to surfaces extending into four dimensions.
Much of the theoretical background material relies on intuition and language typically developed at the graduate level, which required Lee to reach well beyond his coursework. “It was really challenging for me to grasp those ideas at first,” he says, “but looking back, it was a really valuable experience.” The computational side of his research was much more familiar and built on skills he’d developed in his four years at the College. But his work still required him to adapt existing tools to address problems they weren’t originally designed to solve.
That process, Lee says, formed the crux of his learning. “I used to think that bringing something new to math required a completely original approach,” he says. “But through this project, I realized that a lot of progress actually comes from understanding existing methods really well and then applying or adapting them in new contexts.”
In addition to his influence on the project, Lee says Sabloff shaped his evolved view of mathematical thinking. “His ability to tackle new, previously unseen problems and efficiently break down potential solutions has strongly influenced me,” Lee says. He also credits the College’s Department of Mathematics and Statistics as a whole, describing the faculty as consistently approachable and supportive.
After Haverford, Lee plans to pursue graduate studies in computational finance, where the techniques he has honed translate directly to quantitative research. Writing his thesis gave him much more than technical tools, he says. The experience of conducting literature reviews, building a structured research plan, and seeing an independent project through from start to finish gave him a clearer sense of what research actually looks like in practice. The process sharpened the softer skills, he says, that a career in quantitative work will demand.