ForMyThunder said:
Are there any statistics? What's the acceptance rate?
A ball park estimate of the acceptance rate is easy to work out:
A tier 1 research university like Harvard will generally get
at least 500 applicants a year to anyone of it's programs.
From PhDs.org, Harvard Math's incoming class last year consisted of 12 people. Assume they accepted twice as many people as the actually wanted to have in their first year class. (Admissions people are very good at playing this game.) So that puts us at 24 students accepted to the program.
So we have 500 people who think they have what it takes to study at Harvard (and a lot of them probably do). 24 people are actually accepted.
That's a 4.8% acceptance rate!
The Moral
Assuming you have the numbers that make you a potential Harvard applicant, your chance of getting in is
still only around 5%!
Even if you assume the school accepts 3X as many students as they actually want, that only pushed your chances up to: 7.2%
The point is that a "Harvard or Bust" plan is not a good idea. Many, many qualified people will still be disappointed comes time for acceptance letters to be sent out.
The Bright Side
There are many, MANY more great places in the world to study math. They may not have the big names, but they are great schools with great programs. You can go to many schools and find great faculty members, learn a lot of math, physics, etc. and experience a lot of personal growth. And that is what it is about in the end, love of the discipline and personal growth. Trust me, Harvard and Berkley do not have a monopoly on that.