Programmers work with graphs often (file system, greplin, trees, "graph isomorphism problem" (who cares) ). But have you ever tried to construct a simpler building-block (basis) with which graphs could be built? Or at least a different building block to build the same old things.
This <10-page paper also uses 𝔰𝔩₂(ℂ), a simple mathematical object you haven’t heard of, but which is a nice lead-in to an area of real mathematics—rep theory—that (1) contains actual insights (1a) that you aren’t using (2) is simple (3) isn’t pretentious.
I show this paper to college freshmen because
• it’s pictorial
• it’s about an object you mightn’t have considered mathematical
• no calculus, crypto, ML, or pretentious notation
• it’s short
• it’s a classification proof: “How can it be that you know something about _all possible_ X, even the xϵX you haven’t seen yet?’
i
Vipul Vaibhaw