Strictly speaking, applied math is a tool used by science, and especially by physics where it is the essential language in which scientific principles are formulated. There are, however, many areas of mathematics that were originally considered to be abstract only to later be found to have direct application to science, especially functional analysis, spectral theory, and quarternion algebra (among many others).
There are plenty of phenomena that physics as it is currently formulated cannot currently explain or model, and possibly may never be able to describe in a sensible or intuitive way, including the underlying rules of quantum mechanics or the formation of common patterns across broad scales from biological organisms to cosmic structures. However, the reason that we can’t describe them using our science the limitation of our tools and minds, which we apply to try to explain the underlying physics in terms of behaviors and mechanisms that we currently understand. The “wave/particle” duality of quantum mechanics is a great example of this; some people ignorantly suggest that there is a paradox because fundamental particles behave in ways that are both wave-like and as a discrete particle, when in fact they behave the way they do because they are neither strictly a wave or a particle. There is nothing mystical about it except that we are too primitive to fully understand or describe the behavior.
There are a variety of scientists (physicists, cosmologists, biologists, et cetera) who have tried to adopt the language and methods of science to explore mystical or supposedly supernatural phenomena; some like Frank Tipler, Fred Hoyle, and Roger Penrose are even well noted in their particular fields. However, they are left to either advance highly speculative hypotheses that are not falsifiable, or else propose mechanisms for which there is no observational evidence, and thus just end up looking foolish.
There is nothing that innately prevents a scientist from also holding a religious or mystical point of view about supposed phenomena that are beyond the current ability of science to explain or technology to measure, but an honest scientist is always going to have to be willing to revise their beliefs if new data, measurements, or credible mechanisms are proposed to revise formerly mystical phenomena, else they may find themselves in the trap of being disingeneous or outright lying in defense of believe despite objective evidence to the contrary. Most good scientists, however, by dint of personality and training, tend to be skeptical of “because I said so” explanations about gods and magic faries, and thus may find the adoption of dogmatic or literalist religious interpretation to be at odds with a desire to rectify faith with fact.
There is certainly nothing you are going to learn in a university physics course that will reinforced your belief in the religious or supernatural, as such classes shy away from the speculative in favor of practical applications and understanding of the laws of physics as we currently understand them. Although arguements about intrepreations of quantum mechanics get much coverage in the popsci literature, they are covered only very briefly if at all (and then only as historical notes) in actual quantum physics courses because they have no real application to the use of quantum mechanics and offer greater insight only insofar as some interpretations may seem more esthetically pleasing than others. At the final exam, however, the prof wants you to be able to calculate the effects, not speculate on how it might work if you could see beyond the veil of seeming stochastic behavior.
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