Welcome to Gaia! ::

A whole thread all about me! I'm so flattered!

Yeah, I'm an undergrad majoring in mathematics (pure) with a minor in theoretical physics. I branch into other things when I find them to be mathematical enough, such as linguistics or computer science, but my first love is mathematics. To me, there is nothing so beautiful as a tautology stretched thin enough to see through, a shimmering silk made of nothing but daydreams and flights of fancy.

More specifically, if this means anything to you, I'm looking into differential geometry and topology, although this takes me in all sorts of directions thanks to everything actually being algebra or analysis.
I also look into number theory from time to time, simply because number theory is so ludicrous. In a good way.

I am proud to say that I am attending Harvard University, and am having a wonderful time here. The professors are all flakes, and the students are either nuts or preps and it's very easy to tell the difference. Plus, it's got the benefits of being attached to a city, and a good one at that.

As for geometry/topology, I really like what I'm doing in the subject. Geometry makes sense to me. Kinda. Sometimes. At least, differential geometry makes sense to me on occasion. Algebraic geometry just looks kinda weird.
I'm not sure whether I like differential geometry because of GTR, or if it's the other way around, but there's some connection there, no pun intended. I'm hoping to go as far as I can with both.

Do you know what kind of geometry/topology you're doing? I just ask because I have very little experience with algebraic geometry other than a bit of elliptic curves and bits of projective geometry.

Princeton's nice and all, but there's nothing there. By which I mean Princeton the town is basically a row of pubs sitting on the edge of Princeton. How'm I supposed to live there?

Yeah, I'm also having a lot of trouble doing diff. geom. as an undergrad. Plus, it does require a lot of algebraic geometry since a lot of diff. geom. structures just get translated into algebra. It's like everything is being made into homologies and cohomologies for some reason.
Morse theory seems to still be somewhat open, as are bits of symplectic. But yeah, diff. geom. seems to be pretty well traveled.

Yeah, well, I've lived here all of my life, and I quite enjoy being within walking distance of just about anything I want.



There's actually a few neat connections between Morse theory, homology, and knot theory. I just finished an article describing the Heegaard Floer homology, which is built up from Morse theoretic structures, and it has a very nice application to knot theory.

Oh! I didn't mean an article that I wrote. No, it's something that one of the professors dumped on me.
Although some of my friends are putting out minor stuff (it makes me cry, because their fields don't have nearly as much foundational work done as diff. geom. so they can actually write stuff). I'm probably not much farther than you are; other than one absolutely terrible course on real analysis, I've only really taken entry-level undergrad stuff. I'm going to be taking some graduate level courses this coming year, though, but only first/second year graduate. I've been forcibly warned against taking anything more advanced.
But anyway, it's not so much about taking courses as it is about latching onto a professor and bugging him until he gives you stuff to do. That's where I got the article from.
Sorry about the confusion. I'm not that smart.

How long have I been a university student?

Well, according to the system I'm going to be entering third year undergrad this fall. This ignores the fact that I had been taking Harvard classes unofficially for two years before entering (one physics course and three rather laid-back undergrad math courses). It's really kinda stupid since I can't count those courses toward my degree. But then, I didn't get Harvard grades for them, so perhaps it's not so illogical.
It's not like I would have been able to take those classes without very special circumstances. On the other hand, I wouldn't have been able to graduate from high-school without them, since I'd done AP calc by the time I got into high-school, and even with the Harvard classes I had to graduate high-school in three years before I ran out of classes to take.

I don't suppose anyone else is going to be opening up with their life stories? Or should I change the title of the thread to encourage such?

Eh, there was some bull about me not being a Harvard student while still in high-school, and how those classes were supposed to be for high-school credit since I wasn't taking any high-school math courses. I mean, given how much effort it took to simply get me into those classrooms, I'm just grateful that I was allowed to even audit.