In discussing general physics with my tutees, one of the things I emphaaize is that new discoveries in physics often result from "following the math" -- developing experiments to test the consequences of the math, no matter how odd they seem. Two classic examples of this: no one had a clue that matter and energy were exchangable in a fixed ratio until Einstein followed his math and came up with E = Mc^2. No one would have thought such a thing as a black hole could exist until Chandrasekar followed the math and saw that they had to exist if gravity existed. 

In your own work -- Follow the Math!