All three are Ph.D. programs where I'll have more than enough funding to live comfortably without incurring student debt. I have offers at the first two and a waiting list at the second, and I'm trying to decide what my final decision will be. Princeton's program seems to be a little bit like Cornell+, so mostly I'm looking to compare these two what CMU has to offer.
My concern is mostly around the fact that while CMU has the best masters' program for my field and possibly the best thesis advisor for anyone wanting to do stochastic calculus, it's still ranked quite low for mathematics overall, whereas Princeton and Cornell are both Ivy league schools with strong ORIE/FE departments.
