Mathematical notation is much more fluid than programming languages. People make up notations on the spot or abuse notation all the time. This is all done in the interest of uncluttering the maths from any unimportant details so you can focus on the important patterns.

You can see that if you ever try to do actual maths on a computer, e.g. with a CAS or, worse, an automated theorem prover. Suddenly you have to care about all these technical details and you get bogged down quickly.

This is exactly it. The terseness of mathematics, the cognitive efficiency of these notations aren't to be debated, I feel.

I'd rather ignore ad hominem above ;)