One thing that has captured my interest lately is the depth of mathematics. I see questions and answers discussed on Math.SE with so much different notations, terms which seem quite alien to me. Yet, I understand many things and have successfully applied them in many fields, from physics to computer science (and there to computer graphics and 3D interactive applications).
Yet, I find myself baffled by all the terms being thrown around here since I'm self-taught. I would really like to grasp things with more rigour like it is expressed in many answers (and even questions), but I don't know where to start. Isomorphisms, automorphisms, intricate notions of probability theory, measures, non-commutative rings, automorphism groups... Sheesh!
It really seems overwhelming, but is this really the case? If someone could someone point me in the direction of good books, I'd be more than willing to go through things I already have a solid understanding ( I hope ) in order to capture the formal spirit of modern mathematics.
Is such rigour compatible with intuitive understanding? I really appreciate a firm "feel" for any subject. And then when I "learn" to trust it, I can generalize it further.