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Fair point, though I don't think that's really the problem persay. I get discouraged when I feel overwhelming or like I'm underperforming, which was the case at harvard because of the quality of my peers and some emotional immaturity on my part. I perceived a great deal of effortless talent from our IMO guys and other classmates which got to me when I was young. This did change even during my time at college. By my senior year I was taking and enjoying math classes again with students of great calibur. I enjoyed those classes, and I didn't get discouraged. What I meant by that comment is simply this: There is a massive intelligence differential between me and Ph.D students here. I already know from experience what math ph.D's at the ivy league are like, and it's above my paygrade. It takes me longer to learn things, usually many many passes, I wouldn't be able to do research with significantly more classes, etc. The point of that comment wasn't that I don't feel comfortable with smart people, It was just a way of saying "I know what I am not cut out for." Just a statement of acknowledgment re: my limitations and what I need to learn effectively. As for research interests, I really like dynamical systems and slightly less pure mathy stuff than I studied in school. Discrete things, like packing/optimzation and combinatorial problems (reading Wilson&Lint atm). I also wouldn't be planning on going to a Ph.D program immediately. I was more wondering what the best practical path to take would be if I did, after continuing to self-study? Or rather, does there exist such a path, where does it lead, etc.

I went to Harvard as an undergrad, but I was exceedingly poorly prepared in more or less every respect. I ended up finishing with a 3.3 GPA and a 3.1 concentration GPA (My pure math classes are higher (3.45), the lower grade is because I counted four physics classes towards my major that I bombed due to having no background in physics and feeling pressured to try and keep up with the kids in the "advanced" classes.) I stopped taking Math classes after sophomore year due to profound feelings of inadequacy and a bad break-up making me decide to just play piano all day everyday. I took some more math senior year, and did better in those classes than in early ones (Including a few graduate level math classes) I used to really, really like Math. In high school, and for the first few years here. I wasn't doing poorly either, but I was immature and I didn't deal with personal situations well at that point, and music provided an outlet. After I graduated I started rediscovering my affection for math by looking through some of my textbooks in courses I didn't feel I'd mastered in college So damn frustrating. I studied for and took the GRE's and this is how I did. GRE general: 165 verbal 169 quant Math GRE: 890(edited for typo) So that is the one thing I have. I also passed the P exam for actuary qualification although I don't want to do that unless nothing else works out. I've seen the kind of people who are Ph.D students at Harvard so I know for certain that's out of the question, even if by some act of divine intervention I got in I'm not smart enough to hang with that crowd without getting incredibly discouraged. I took classes on: real analysis, theoretical linear algebra, complex analysis (UG and graduate level), abstract algebra, combinatorics, and differential geometry. I took physics but I sucked at it (No grades about B+ and a few C's) My other grades in math classes were good except for abstract algebra. I have no research experience, I did musical things during the summers. I know a few professors but they can't say anything about me but "Did pretty well in my class." Is applying worth the application fee? Is there anything I can do now to make myself a better candidate?