The conclusion of Eugene Wigner’s paper: The unreasonable effectiveness of mathematics in the natural sciences.
The miracle of the appropriateness of the language of
mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning.
There has been a long history of applying (particularly geometrical) mathematical techniques to study physics. In this program, Marina Logares has just published a paper: Symplectic Geometry of a Moduli Space of Framed Higgs Bundles