Having been an avid lover of Mathematics, it is my dream to become a mathematician one day. It is purely passion that drives me and I just can't stand the thought of not doing math when I grow older. Because of that, i have been learning some "Advanced Mathematics" (Real Analysis and some Abstract Algebra mostly, and a little bit of Linear Algebra).
The first thing that any guy jumping from High School Math to proof based, rigorous math, should notice is how different they are from each other. Math that I am learning now is definitely not like the Math that I now do at school. This is the fist thing I realized when I started doing Real Analysis a few months back.
Advanced Math, I noticed, is exceptionally beautiful and at times it is like art, utterly elegant and aesthetically pleasing to the eye(and the mind:)). I don't know if others share this same feeling with me. I used to enjoy Math then, for sure, but nothing compared to the enjoyment I am having now.(for more elaboration of my "enjoyment" please look at my profile's About Me section :))
Because of the enjoyment I get while doing Math, I am pretty much sure that I would like to major in math someday and if possible go to a graduate school in mathematics.
But this being said, I do have a small concern. Because Higher Math is so very different from grade-school math, I fear that as I dive in deeper and deeper into mathematics, I might realize that the Math I do then has changed so much that it was nowhere close to the Math that appealed me. How substantial is this fear? Is it legitimate?
Because this community is full of Mathematicians,(and people at MO don't seem to like these kinds of questions, they close it straight away) I figured this would be the best place to ask If you guys experienced such a feeling too? How and in what ways did you find math different from fairly lower level math that I am currently into. (Please note that my Mathematical knowledge isn't that rudimentary either. I have taken an "Advanced Math" course in High school and I do study math during spare time as well, for fun :))
Note: You might say that I can always change my area of study when I get into college but as I mentioned earlier, "...I just can't stand the thought of not doing math when I grow older..." So If it is that Math isn't what i actually like, I'd like to have time to get used to it. I think it makes sense!
Any help is much appreciated!
Thanks in Advanced!