It's hard to explain, it's the way you think and talk about math, it's not about visible signs like notation.

I like the Scott Bakker analogy for magic, there is the visible part of math (formulas, etc.), and the corresponding mental habits. The visible part without the correct way of thinking behind the scenes doesn't work.

I guess one example is an ontology of "the type of math that's being done" in one's head, that lets people quickly figure out what the paper is trying to do after reading relatively little of it.