When I think back on my mathematical education, there are a few key experiences that stand out. For example, the time when, as an undergraduate out on a walk, someone explained the 100 Lockers Problem to me, and I stayed up late thinking about large cycles in random permutations. The time that I asked about the remainder theorem in the context of principal ideal domains, and got a respectable answer from a professor on the bus. Or getting excited about the movement of ink in water, and asking some friends to play with an ice bath and indian ink in the lounge. All of these experience had a certain informal-ness to them, a certain off-the-cuff, improvisational character. For me, they were humane, relational, pleasurable, and formative mathematical experiences.
Recently, I’ve been reading about amateur magicians' techniques for repertoire management. The ways that they keep a hundred tricks in mind, and deploy them when the moment is right. There is a sense of cultivation, maintaining a garden full of ideas, creating human relationships with an audience, and an awareness of when to launch in to material. And this has me thinking: what would all that look like for mathematical experiences?
There are a bunch of simple things that don’t come up in the undergraduate curriculum, but are thought-provoking and worth sharing. It would be an interesting exercise to compile a list of these, practice them a bit, and learn to make them come alive for other people. The sorts of things that I’m thinking of are: sundials, the platonic solid groups, continued fractions, the golden ratio, the dragon curve, etc.
It is pretty meta and geeky to make a list, check it twice, and hone these micro-experiences. But why not? If you’re teaching faculty, and spend a lot of time around students, then creating mathematical experiences is part of the job. I’m going to keep pondering the idea of carefully crafted mathematical experiences, and play around with it. I think some avenues worth reading about to further this project would be improv and bits in stand-up comedy.
Published: Jul 16, 2024
Last Modified: Jul 17, 2024
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