If all you have is a data encoding method....

Realization: Polynomials and indexed arrays of integers are, if not isomorphic, then *very* useful for understanding each other.

I'm kind of embarrassed that it took my brain this long to explicitly put that one together. Which is to say, I always knew it, but I didn't previously realize the cool stuff that falls out of it, like taking the derivative to move the index into the coefficient, etc.

This is (apparently) what I do on vacation. Happy New Year!