It seems I've got to the point where I no longer see the immediate applications of theorems. I study actuarial science and am attempting to describe probability and measure theory more intuitively but then I come across theorems like Radon-Nikodym whose immediate applications escape me.
Is this a usual thing for the average mathematics student? Does practicing make me a math fraud who just learns to identify rather than reason. I feel incomplete if I can't apply it to a completely new and foreign situation without needing exercises.
How do gifted students, and obviously I'm not the caliber of Terrence Tao, but what makes his understanding different?
