It is very difficult to attend top mathematics graduate schools. The graduate students at Berkeley have astonishing records:
- One student graduated as a triple major in Physics, Chemistry and Mathematics with a near perfect GPA, all with honors (and all with honors theses) from a top university.
- Another student graduated as a Mathematics major from Cal Tech with a perfect 4.0 GPA.
- Another student went to UC Berkeley for undergrad and had a near perfect GPA and began taking graduate courses his sophomore year.
... And the truth is that a lot of these students wouldn't be going to Berkeley had they been accepted to Princeton.
So, yes, it is unbelievably difficult to go to a top graduate school for mathematics.
It would require a near perfect GPA, 6 or more graduate courses, and research (all done at a top undergrad program).
A conversation that an undergrad friend from Berkeley had with her major advisor (who is a math professor at Berkeley):
- Professor: "So, what do you want to do?"
- Student: "Go to grad school."
- Professor: "In math or stats?"
- Student: "Math, ideally."
- Professor: "What's your GPA?"
- Student: "3.8"
- Professor: "I think that's a little low for a top math grad school."
- Student: "What would I need?"
- Professor: "Maybe a 4.0?"