(June 7, 2018 at 10:42 pm)Kernel Sohcahtoa Wrote: CIJS,
I've completed my self-study of real analysis. The subjects that I covered during this fascinating intellectual odyssey were the properties of real numbers, basic topology of the real numbers, sequences, series, functional limits, continuity, differentiation, and Riemann integration. The final topic that I studied and was actually able to appreciate and understand via relevant definitions, propositions, theorems, mathematical ideas, etc., was the fundamental theorem of calculus (FTC). I can't believe that the theoretical beauty of this wonderful idea had eluded me when I first studied calculus: my computational mindset inhibited my ability to appreciate the harmony of mathematical concepts and ideas that make the FTC work.
That said, I must say that learning real analysis has given me a much greater appreciation for the originality, creativity, perseverance, and wonder that is involved in successfully constructing convincing proofs that establish the truth of mathematical statements; I'm truly in awe of those individuals who are gifted at proof-based mathematics.
Many kudos for you efforts. You will become "gifted" at proof-based (theoretical) mathematics by doing proofs. There are only so many types; until you get to some of the really involved things that take a person making mathematics their life well before they got to your age. I'm not one of them, either, btw. A cruise through geometry and linear algebra will see you well on your way to having a handle on doing proofs, believe me.
As far as the beauty eluding you at the time, I'd have to say that being under time pressure to get the material under your belt in time for tests, coupled with your "real-life" activities interfered with that. It wasn't until I was teaching geometry and algebra/math analysis that I had the time to work on it and get that feeling of beauty. I know that is how it was for me, anyway.
If you get to thinking you’re a person of some influence, try ordering somebody else’s dog around.