Topics for Nonstandard Math Study?

[in-a-box]

TL;DR:

I was a severely under-motivated student all the way through high school. I was obsessed with math and science as a wee lad, and dreamed of going to MIT. Well, perhaps I was a little too obsessed. Early on, my teachers were telling my parents that I could probably teach the class better than they could, yet at the same time they couldn't pry me from my book of interest and get me to do any actual work. This theme continued all the way through elementary and middle school. Worse, despite my passion (or perhaps because of it), social problems plagued my early life. Unable to cope with my perpetual alienation from my peers, my focus turned entirely onto my social issues. I was officially diagnosed with (high functioning) autism at age 7, and since that day have fought tooth and nail to get to the point where I could function properly in a normal social situation. It's been absolute hell, but I'd say that goal has been sufficiently reached.

I got through high school with okay stats. I admit that I fully deserved those stats; I hardly ever studied or worked. Maybe I had good reasons, or maybe I didn't, but in any case I'm left feeling like I completely wasted quite a few years of academic potential. I brooded about this at first, but I'm starting to find my path. I have a 4.0 GPA at my local community college, got hired as a math tutor pretty much on the spot after my second Calc I lecture, and am president of the school's math club (the youngest club president in the school, I might add). I hope to pursue a dual BS in math and physics starting next fall.

Unfortunately, I'm left with (what I feel is) a bit of a dilemma. I still feel fairly behind in math. I have the standard k-12 math curriculum down fine, but there are many topics that seem interesting and important that I feel I should've touched on years ago. Am I right in thinking this? Topics like "these"[/URL], or the topics covered in Courant's book "What is Mathematics?" come to mind. Is it worth my while to learn such topics now, or is it kind of "too late" in that I should just wait to cover them in depth in college?

 

[Perturbator]

It is most certainly NOT too late. I didn't get serious about studying math until the summer after my sophomore year in college. In fact, "What is Mathematics" was the book that came to mind when I read the first bit of your post---It was the book that got me fired up and interested in math. I would also recommend George Comenetz's "Calculus: The elements". Those two books changed my life and the latter helps far more than you'd think with physics intuition.

Background: I dropped out of high school then went to college a few years later and nearly failed out---I read these two books one summer and changed my life. I'm now currently working on my PhD.