Physics also gets caught up in the elegant end result of a theory, that likely started out as a messy idea, and while Physics & Maths benefit from each other, however, Physics is not Maths.
The current problem facing Physics is that there seems to be too much distance between what the experimentalists can do, and what the theorists believe.
(a.) Physics focuses on precise measurement, aimed at specifying values of defined physical quantities: this is the work of quantitative experimental physics, and ensures the descriptive accuracy of physics.
The stark separation of Physics from Metaphysics always seemed a bit odd to me: considering that Metaphysics is "beyond Physics", there should be a bridge between the two, so that there can always be information shared about what belongs to who, and where that boundary is.
Due to the deep interrelation of Mathematics and Physics, there is inherent tension between the two fields, perceived by mathematicians, physicists and mathematical physicists. Also, an attempt is made to explain why mathematical rigor is typically unwelcome in Physics.
These debates impacted Physics greatly: mathematics is the language of physics, and platonism makes speaking about time challenging. This led to the expulsion of the concept of time in physics: all events are the consequence of quantum fluctuations that took place during the big bang.