I am a current high school senior choosing between attending MIT, Princeton, or Yale for my undergrad. My current goal throughout and post undergrad is to secure a summer internship at one of the big NYC quant hedge funds (Jane Street, D.E. Shaw, Two Sigma) and hopefully transition into a full-time offer after graduating. Out of my three choices, which college would be most conducive to this kind of career path, and what majors and activities specific to this college choice would be most conducive to this kind of career path? To a lesser degree, which college would provide the most versatility if I decide to deviate from this career path and do something else within STEM? I am mainly choosing between MIT and Princeton and have knocked Yale out of the equation, but if Yale has some low-key advantages that I don't yet know about, then I am willing to reconsider it.
I should add that at any of these colleges, I intend to major in math or any interdisciplinary subject that is primarily math. I am also considering ORFE at Princeton.
I would greatly appreciate any advice. Thanks for your help!