Physics started out with aim to describe and predict the motions of the common objects and and the heavenly bodies (planets, stars).
However, Mathematics existed mainly in form algebraic equations. And Mathematicians loved to ponder over abstract things. Pure Mathematicians enjoyed much time in trying to wrangle around abstract symbols, equalities, inequalities and laws governing those.
Physics uses extensively the ideas from Mathematics to model the phenomenon as abstract frameworks, applies the laws known within the Mathematics and tries to predict the outcomes and then observes and calculates and compare if something wrong or right.
Back in 1900s when Black Body radiation problem caused a trouble, “physicists” used calculus to explain these ideas. But It fails to explained until Max Planck used quantisation of energy as fundamental structure which existed in reality. This was discerned by the impossible existence of ultraviolet catastrophe. But it sends us important hint that if we alone base our calculation on mathematics, it would lead astray us from our scientific goal.
Similarly notion of the existence of imaginary numbers caused great discomfort to realism. But today we know they exists and calling them imaginary was just weak philosophical understanding of that time.
However, reality of sub atomic particle (quantum mechanics esp. Wave Function) was intricate to both our physical and mathematical understanding of the foundation of nature. We have resorted to so many “Interpretations” that it is becoming fashionable to come up with some totally funny interpretations. In such cases we only have one way to distinguish the truth from chaffs to physically test, falsify and use them in practical applications and make/measure real predictions (turn to physics).
Sorry, “Shut up and calculate” gang. Humans will need to engineer tech to falsify/test interpretations like the way Michelson Morley did, like Galilean telescope did and like many other physicist/engineers did.
We human need few centuries to actually figure out the the tech to engineer instruments and test the physical interpretations of wave functions collapse.
Till then let physics and mathematics be rivalries to each other.
