Theromes do exist but always with a defined set of starting axioms and therefore a theorome when applied to the physical world becomes a theory.
Theorems and theories are two different things. You're quite right, that proving a theorem requires a well-defined set of axioms; the natural world, unfortunately, doesn't provide us with such axioms*, which is why we have to use theories to describe it.
*Well, maybe. "The unreasonable effectiveness of mathematics" argues that maybe there is some axiomatic Truth at the basis of reality. But if so, we have no idea what it is yet, and anyone who tells you they know is lying.