I'm a math and physics major, just finishing up my freshman and having a great time with what I'm studying. After working very hard, I've finally managed to get basic classical physics through my head - Newtonian and Lagrangian mechanics, electrodynamics, some relativity - and it's a joy to see it all come together. I honestly marvel at the fact that, to good approximation, my environment can be described by that handful of classical equations. Everything above them is phenomenology, and everything below is a deeper, more careful approximation. Sure, I could never learn it all, not even close, but none of it is beyond arm's reach and a few years of study.

But in math, I get the opposite impression. I've studied through linear algebra, vector calculus, differential equations, elementary analysis, and a survey of applied math (special functions, PDE's, complex functions/variables, numerical methods, tensors, and so on) required of physics majors. And right now, I can't shake the feeling that the field is just so prohibitively broad that even the most talented mathematician would be very lucky if the tiny fraction that they spend their life on were where answers lie.

Maybe this is just something everyone goes through once they're one the threshold of modern mathematics, as I think I can fairly say I am. Maybe I'm wrong, and if I'm patient and keep studying it will all seem to come together. Maybe something else. Whatever the case, any words - kind, wise, or just true - would be appreciated.