By any reasonable standard, nobody in the classroom would resist the striking artistry that the equations had proven to us. I had often wondered what it took to make such complex equations that are complainant to reality. Now I know and wish I knew it earlier.
In order to make an equation that is complaisnt to reality, a physicist runs experiment, measures data points, plots the data points, figures out a mathematical expressions that when plotted, matches the data points. This is what experimentalist do.
The second strategy involve a theorist looking at a whole bunch of different specific equations, which arise from doing all sort of specific experiment, and tries to look for mathematical patterns. If the physicist is lucky and clever, he or she can see a pattern and write down a general equation which when applied to different situations, reduce down to the various specific equations.
If the physicist had done a good job,he or she can find a general expressions that will be true in all situation—as long as the rules of maths and physics are carefully defined and applied.
So, a physicist job is to work out premises which follows nature. He or she does this by manipulating the premises mathematically and finding the relationship. Either observation follows the prediction or they don’t. If they don’t, no matter how elegant the math is, one proposition was just wrong.