I think it’s just that what’s being talked about is so precise and so deep in the weeds of nested definitions that you generally need to talk like that, or at least you have to be a truly gifted communicator to write a math paper without it.
>or at least you have to be a truly gifted communicator to write a math paper without it.
i know a lot of math (hence the name) - basically lots of stuff scattered around analysis, geometry, and complexity theory, at varying levels between senior undergrad and research level (MIP and SAT and SMT). this basically tracks my academic progression (from math undergrad to cs phd student).
the stuff that i can explain the best is the research level stuff. why? because i can explain it in the same relatable terms that i learned it through, since i learned it when i needed it - through relatable examples that clearly motivate the ideas. i've done it many times - often a junior phd student will ask me what i work on and i start telling a story that starts with some really common thing that gives a foothold ("how would you figure out which variables in a for loop are reused") and then step by step you "follow your nose" to the ideas behind the proofs and techniques and etc.
what's my point? lots of academic math is useless frippery that couldn't be motivated in this way and so it can't be articulated except formally.
If you want to explain something in a loose fashion, that works.
It doesn’t work so much for proofs in a lot of mathematics, especially because the “common ground” you speak pf starting at would be hours of explanation behind what you’re trying to say.
