If you'd like I can contact an old client of mine, Paul Seidel...???
Prof. of mathematics at MIT....
Depends upon what you want to do. MIT will take you down the hardcore STEM path while Princeton is probably a better choice if you are looking to teach/research using Math.
If this is *very* important to you why do you ask us EP people with no clue on Topology/Chaos Thery and Cosmology/QM??
Be careful about early admission. If they get you to say yes, your money package is likely to be less than if you proceed on the normal time path. However, Princeton is known for being the most generous with non-load monies. Of course, if you don't need assistance, then by all means charge forward with the early stuff.
Go for the school with the professors who will help you get what you are looking for. I realize that this can be a tough choice. There are also schools on the West Coast -- and even in fly-by country -- that would fill your need.
Given your means, maybe you should visit -- and I don't mean officially, as in with an escort -- the schools of interest. Hang out. Maybe you have friends who are already at those schools. I know people who LOVE MIT. My mom is one of them. I also have a friend who did his graduate EE (really CS) work at Princeton, and is quite happy with the results.
Do you like hanging out, talking about this stuff into the night? Maybe MIT is the place? Could be Princeton? Could be a Claremont college like Harvey Mudd? All excellent, but you won't have any real idea of which one will do the trick unless you visit. And you have the luxury of visiting.
Hope this helps.
A fun situation to be in. So, have fun and good luck.
MIT for sure.
Apply to both just in case, you never know. If both come back take a coin and do the "fractically minded mathematical" thing.....flip the coin in the air, call it, done. Seriously, life IS about "taking chances!" LOL ;D
I might have suggested doing an 'Istikhara' but I guess you don't believe in that stuff. So go with Princeton 1st.
MIT hands down
Make a pros and cons list for each.