You’re heading deeper into the philosophy/study of knowledge which is called Epistemology.
What I think you’re trying to say is you think there’s a divide between sciences which deal with making models about “reality” and testing them versus the sciences like logic and abstract mathematics which constructively discover truth by deriving it from previous truths (axioms/theorems).
However, in a very general sense, any logic whatsoever—written symbolically or in natural language—is mathematics. Making the assumption “matter/energy is not created nor destroyed” and then using that assumption (axiom) to derive “momentum must be conserved in a collision” is mathematics just as much as it is physics. Any time you build ideas on/using a “scientific model” you are using logic/mathematics.