The Pythagorean mystique of mathematics runs deep as one of our secular religions.
mathematics is certainly a reasoning system – and it is very complex and messy in places but there’s usually a way around.
many of the developments in mathematics were to solve physics or other problems – or rather to model – not so it always resolves to physics but always to itself and often to physics :
so if you build on top of a physics modeling system that resolves to itself but sometimes to physics too, it is exactly the kind of substance to build physics models with.
some question comes up in physics.
math model is made. sometimes a new math needs to be devised.
The physics question is answered and now there is a new math tool to build with.
New math tools build on top of those math tools which had been built to model physics.
and again these tools end up being useful for physics.
then more math concepts are added on top of THOSE etc.
its been scaffolding for each other since the late medieval times for sure.
Even back to Pythagoras, much of his work started as engineering solutions.