Did there exist and does there still exist a debate over which school of mathematical thought (i.e. formalism, logicism, intuitionism, etc.) had the most affinity or application for physics? In particular, I am looking at if a case can be made linking one these schools of mathematical thought can be linked to physics discoveries during the first half of the 20th century such as Einstein's discoveries of general relativity.
One such debate opposed the historian Geoffrey Hellman and constructivists like Douglas Bridges; see e.g., the article
Hellman, Geoffrey. Quantum mechanical unbounded operators and constructive mathematics—a rejoinder to Bridges. J. Philos. Logic 26 (1997), no. 2, 121–127.