My Path into Physics (at MIT)

I started liking math since the day we first learned how to solve linear equations in 7th grade (we actually had a sub who just gave us a sheet and we pretty much had to do it ourselves, and I'm sitting there like "... what do you do, just guess n check?" but then the next day our teacher showed us a logical way/procedure to solve all of them. That's what drew me in.Then all throughout HS I would shut myself out and just read dr math and math "armchair books". I really enjoyed its beauty and wanted to see a simpler, more intuitive path as to why theorems worked the way they did (Basel problem is my favorite). I wanted math to seem more intuitive.In my undergrad classes (majored in math lolz), I realized that we sometimes "relearn" the same concepts and what not. I just ended up more confused after I graduated than when I entered, with all my naiveness. I wanted to know roughly in what order to learn concepts once and for all, and in an intuitive, non circular-seeming way. And apart from that, a lot of subtle things would confuse me also (one thing was why, when doing "set equality proofs" we use both the same letter in showing inclusion and the reverse inclusion. I later learned that it was because of "quantifier scope").So my ultimate goal is to understand in an intuitive way why it is that math works, and to be able to start from the bottom (some reasonable bottom...) and build it back up (not formally, since incompleteness doesn't allow you, but just in an "informally rigorous" way). I want to see why its theorems work, and where they reasonably come from. Plus, I have OCD, so my need for organization and seeing perfection in objects is what runs my life really.Ps, I also do like physics, but it would just confuse me too damn much in subtle ways. I mean, math does too, but at least we have exact definitions and such in math, making it somewhat more manageable! :P