Many of my friends went to Harvard/Yale/Princeton/MIT/Stanford.* I also went to one of those schools. Occasionally, for fun, we compare our college experiences. Our conclusion is that there are differences between them that are meaningful but not deal-breaking.
Given your academics interests, I would recommend Yale least. Other than that, any of those schools will give you fine preparation for a math/physics/CS degree. A fact you can weight weakly is that Princeton’s (non-theory) CS program is relatively weak but its math program is extremely strong. The MIT graduates I know tend to be weaker at understanding foreign policy/economics/the arts, perhaps because no undergraduates study those subjects at MIT. I expect you will be able to take graduate classes and feel academically challenged at any of these schools.
The thing that I’ve heard the most variance on is how happy people were in college, and how many smart, fun and insightful friends they met while there. The main reason I’d advise applying to more colleges is so that you can visit each of them in April and pick the one that you feel like you enjoy the most, because the social experience can be very variable (MIT tends to hyper-sort people into groups of very similar people, Princeton has eating clubs, Stanford used to have lots of interesting living groups but might be growing more boring, Harvard aiui randomizes living groups and they feel a little undifferentiated as a result).
*I don’t know anything about Harvey Mudd, unfortunately. There are other schools that might be a better fit for you which you should obviously also apply to, but these are the ones that I would consider to be meaningful competitors to Harvard.
Many of my friends went to Harvard/Yale/Princeton/MIT/Stanford.* I also went to one of those schools. Occasionally, for fun, we compare our college experiences. Our conclusion is that there are differences between them that are meaningful but not deal-breaking.
Given your academics interests, I would recommend Yale least. Other than that, any of those schools will give you fine preparation for a math/physics/CS degree. A fact you can weight weakly is that Princeton’s (non-theory) CS program is relatively weak but its math program is extremely strong. The MIT graduates I know tend to be weaker at understanding foreign policy/economics/the arts, perhaps because no undergraduates study those subjects at MIT. I expect you will be able to take graduate classes and feel academically challenged at any of these schools.
The thing that I’ve heard the most variance on is how happy people were in college, and how many smart, fun and insightful friends they met while there. The main reason I’d advise applying to more colleges is so that you can visit each of them in April and pick the one that you feel like you enjoy the most, because the social experience can be very variable (MIT tends to hyper-sort people into groups of very similar people, Princeton has eating clubs, Stanford used to have lots of interesting living groups but might be growing more boring, Harvard aiui randomizes living groups and they feel a little undifferentiated as a result).
*I don’t know anything about Harvey Mudd, unfortunately. There are other schools that might be a better fit for you which you should obviously also apply to, but these are the ones that I would consider to be meaningful competitors to Harvard.