You have a weird definition of "smuggling". I say it outright. Because I follow it up with a description of the actual practice of math: it's the study of abstraction. That's not a frame. That's just what math is.

I think the nature of mathematics is an interesting question without one clean answer. To present a radically different view of mathematics:

It's a game of string transformations, where the goal is to produce specific strings given a set of rules.

The (syntactically valid) strings would correspond to statements, a producible string a theorem, and the production the proof.