Any scientific theory admits isomorphism to some mathematical structure in a way constructive (that is not as a proof of “pure existence” in a mathematical sense).

If any theory admits to be represented as the finite intension of a rather extended notion, the proof is trivial: Being finite, the intension can be always well-ordered to a single syllogism, the first element of which is interpretable as “first principles” (axioms): Those axioms generate a mathematical structure isomorphic to the theory at issue.

If one admits the axiom of choice, any intension can be well-ordered even being infinite. However, then the structure isomorphic to the theory would exist only “purely”, which is practically useless.

In fact, any theory even as a description in humanities, philosophy or history is some finite text. This does not imply, though, that some finite extension corresponds to it for any text admits links to its context unlimitedly. Properly, this third case is what is worth to be proved mathematically.