i'm a senior in high school right now, and i have the academic ability to get into some good schools, unfortunately my family does not have the fiscal ability to send me there (even with financial aid), so i will be attending UF next year. Still a good school though. I'll be a math major. My question is, assuming (and this is a big assumption, but i'm just curious) that i do everything right at UF and get a stellar GPA, taking even a few graduate courses, do research, do well in the Putnam, do some REUs/internships, get a great GRE score, and in short somehow pull off the perfect 4 years at UF, will i be able to get into a top grad school (princeton, harvard, MIT, Stanford, etc.)? I know i'll be facing a little adversity here, i just want to know if it's even possible. I know recs are a big part of getting into a graduate school, and UF professors probably wouldn't be as renowned as people from top undergrad schools, so i'm just wondering how much of a shot i'd really have, assuming a really good undergraduate resume. Thanks!!