String theory has long occupied an ambiguous position: it lacks experimental support, so it is not a traditional physical theory; nor is it a strictly mathematical one, since it is not derived from first principles. This article argues that string theory constitutes a third type of entity—an “idealized mathematical physics”—that emerges from the historical separation between physics and mathematics. The argument rests on a four-dimensional analysis: the presuppositional nature of physical theories, the relativity of mathematical axioms, the structural turn in the history of physics (from the S‑matrix program to modern on-shell approaches), and the epistemological framework of structural realism. It further shows that string theory reveals a deep paradigm shift from a model–experiment approach to a constraints–consistency approach, in which theories are no longer selected by experiment but by structural constraints. The ultimate predicament of string theory is not the lack of experimental verification, but the loss of naturalness: when a theory’s necessity comes solely from mathematical self‑consistency, it no longer singles out our world, but yields the sum of all possible worlds. The identity crisis of string theory is thus a concentrated symptom of the soul‑searching crisis of modern theoretical physics.