The Consequences of Assumptions
Lorelei Koss with her award-winning watch bands, in Tome Hall, home to the Department of Mathematics. Photo by Dan Loh.
OFFICE HOURS: Professor of Mathematics Lorelei Koss
Professor of Mathematics Lorelei Koss earned her Ph.D. at the University of North Carolina at Chapel Hill. Her scholarship concentrates on ergodic theory and complex dynamical systems, and her current courses include Multivariable Calculus and Integration & Infinite Series. Over her career, she has published dozens of articles, such as Ordinary Differential Equations and Easter Island: A Survey of Recent Research Developments on the Relationship Between Humans, Trees and Rats and Crowdsourcing Solutions in the Online Mathematics Classroom.
Your research now focuses on things like parametrized dynamics of meromorphic functions, which 99.9999999999999% of people on Earth don’t understand. What makes Dickinson the place to figure it all out for students currently living in the 0.0000000000001%?
What makes Dickinson a good place for this work is not that students are specialists but that they are encouraged to take difficult ideas seriously. Students here don’t encounter mathematics as something finished and untouchable. They learn it from people who are still actively working through open questions themselves.
My research keeps me connected to how mathematics actually happens. That matters in the classroom because it shapes how I teach, even at the introductory level. I’m not trying to turn calculus into my research area. I’m trying to show students how mathematicians reason and how they respond when intuition breaks down.
Dickinson values teaching that is both rigorous and reflective. That combination gives students, whether or not they become mathematicians, a chance to understand how abstract knowledge is built and communicated. Those habits of thought travel well beyond mathematics.
You’re up to things most mathematicians aren’t, like mixing differential equations with music and dance and designing “cellular automata” watch bands (which just won first place at Australia’s CARMA-Matrix Maths Art Competition and was accepted into the juried art exhibition at the 2026 American Mathematical Society Joint Mathematics Meetings in Washington, D.C.). What makes you see math as something that can extend into the world in unique ways?
I think the boundaries between disciplines are somewhat artificial. I started by looking for ways to help students experience mathematical ideas, not just manipulate symbols on a page. That led me to ask what happens when mathematical structure becomes something you can see, hear or interact with.
Across different projects, I’ve used ideas from differential equations to think about literature, film, music, dance and visual design. The goal is not to explain art mathematically but to explore how patterns of change appear across very different forms. For students with strong mathematical backgrounds, this offers another way into the arts and humanities. For others, it provides an encounter with mathematics that does not depend on technical notation.
The cellular automata watch bands grew out of the same question. Each band was designed to reflect a defining feature of the watch it accompanies. For example, Apple Watches incorporate cryptographic techniques into their design. For this watch, each side of the band encodes a hidden message. The project was an attempt to make the mathematical ideas already present in everyday technology visible and tangible.
Mathematics seems to have its fingers in every pie humanity can bake. Is there anything math can’t do?!
Mathematics is an extraordinarily powerful tool for precise reasoning. It excels at working out the consequences of assumptions. What it cannot do is decide which assumptions matter or how its results should be interpreted. Mathematics cannot tell us what is meaningful or what is valuable.
Even within mathematics, there are limits. There are true statements that cannot be proved from accepted axioms, and there are deterministic systems whose future behavior cannot be reliably predicted. Mathematics can describe structure and pattern, but it cannot tell us why a piece of music moves us or why a joke is funny.
What makes mathematics remarkable is not that it does everything but that it does one thing exceptionally well: It gives us a way to reason carefully in situations that are otherwise hard to pin down. Used well, it does not replace human judgment or creativity but works alongside them.
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Published January 27, 2026