any of you nerds occupy yourselves with shit like this?

When I'm in a class and don't have a lot to write down but still want to be using my hands, I usually either

Write out a payoff matrix for a 4×4 or 5×5 normal-form game and then try to find all the pure and mixed Nash equilibria, or

Draw a four- or five-vertex directed graph, label the edges with fractions, then write out the transition matrix and calculate the evolution of the system for a handful of time steps

The nice thing about both of these is that they're very "busy" but don't require serious attention, so they're like the math equivalent of worrying a chew toy. I'll probably get tired of these after a while and need to find something else, but I feel like this is at least more enriching than the very space-consuming tesselations I used to fill notebooks with in undergrad.

When I was bored in high school I would encipher texts with a substitution cipher that shifted forward with each letter (so "AAAAA" would be enciphered as "ABCDEF" and "HELLO WORLD" would become "HFNOS BUYTM"). Obviously this is useless as real encryption, but it does frustrate basic frequency analysis if the text is short enough. It consumes a moderate number of background CPU cycles and if you do it enough you derive all kinds of tricks and shortcuts to speed up the process, which made for nice occasional eureka moments to break up the rote part of it.

When I'm bored and have only a pen and paper at my fingertips I sketch out phonologies and evolve them. Start with a phoneme inventory, syllable structure and a few paradigms. Then apply sound changes as desired and see how the paradigms end up. Level analogically, repeat. You can get through a few millennia in the span of a boring lecture or, alternatively, generate a half-dozen daughterlangs with interesting cognate sets. Doing this habitually for years has made me not only a better conlanger but also given me a kind of immediate intuition for diachronics that's very useful in linguistics proper. Highly recommended.