“To what extent does the place of undergraduate education matter for admission to top graduate programs,”
When I was a graduate student at Stanford, there were other graduate students there who had done their undergrad all over the place. It didn’t seem to make all that much difference. I suspect that the several students who had done undergrad at Rutgers might have had a higher GPA as an undergrad compared to the one guy who had done undergrad at MIT, but not necessarily any higher than he would have gotten had he also gone to Rutgers. Not going too far into debt for their Bachelor’s degree was probably a good thing however. Someone I know who did their MD at McGill said the same thing, that MD students there had done undergrad at a wide range of universities.
“I am going to pursue my career in one of three fields: neuroscience (in particular, cognitive science), mathematics, or philosophy.”
I am not concerned at all about the fact that you haven’t picked one. You are in high school. To me these are all very interesting fields and I can certainly see you being interested in all. You will have plenty of time to pick one.
“Were you actually admitted to an Ivy?”
I was wondering this also. If not, then I wouldn’t worry about it. Try to do very well as an undergrad, and see where it takes you.
Good luck with this.