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

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?