What do you mean that mathematics cannot be used to construct reasonable models of the quantum world? What else is used to construct those models?
I don't understand why you appear to be suggesting that mathematics stops working at the quantum level. To my knowledge it does not, in fact it's so reliable that we pretty much explore the quantum world exclusively with mathematical modeling.
Nothing we have discovered relative to quantum phenomena has rendered invalid one iota of mathematics. Mathematics doesn't have some preference for the macroscopic over the quantum world any more than science deciding that the heavens were heliocentric rather than geocentric revealed any problems in mathematics.
IMO you are confusing mathematics with physics. The science of physics is what explodes due to paradigm shift every few centuries and has to be put back together from scratch... mathematics continues working through it all with at most some new notation being desirable.
P.S. I also do not regard mathematics to be some sort of science. They're completely different things. Mathematics isn't established or expanded by the scientific method nor are its conclusions tested by experimentation as those of science are.