In physics, the physical questions are inseparably joined with their mathematical reformulation. Not only does it provide an exact language, it enables to set off into the areas inaccessible to a plain reasoning, in particular in the physics of the microworld.
The paradigmatic turning points were, as a rule, accompanied by a new mathematical framework. Important physical discoveries were often stimulated not so much by an accumulated empirical matter as by a speculative idea inspired and supported by the mathematical formalism.
Up to now, the evolution of physics fully corroborates this unique blending of physics and mathematics, the Wigner's "miracle", regardless of its metaphysical justifications.