It's interesting that we can start with some stuff, get mathematical conclusions, and then the mathematical conclusions lead to results about Physics. That's crazy! Well, not really, but it's cool, right?
But it's mostly used as a humorous snowclone here. So yeah, it is what it is, and you must remain peeved. There is no relief.
I think physics starts with some very basic assumptions about the world because that's what the world looks like. So I don't find it surprising that the models physics starts with, and their consequences would already have been investigated by mathematicians.
What is a physics problem if not a math-problem? So I never really understood the point of mathematics being unreasonably effective. What am I missing?