I agree with you and the OP that creating a standard notation for all math is problematic. And you're right that there are conceptual difficulties behind the m

I agree with you and the OP that creating a standard notation for all math is problematic. And you're right that there are conceptual difficulties behind the math that are not going to be automatically resolved by clearer communication. But a lot of the difficulties are accidents of culture. To continue the programming language/mathematical notation allegory, you can use whatever notation you want to describe your program in a Lisp with macros. But you have to actually define what your notation means. Neglecting to provide the definition of the macros would be the equivalent of a logical argument that leaves off its premises or the state of math publications today from the perspective of the poor sap that has to read them (and the mind of the person who wrote it).