[kvathupo]

Although I agree that the average student at one of those schools is much better than one at a lower ranked school, I think there is a false equivalency at play here. Enrollees in Math55 are not representative of all math students at Harvard.

In my experience, the average student of a prestigious institution is just as good as an upper decile student from a decent university. That said, the top end of those at top colleges are truly world-class. At the end of the day, these universities have historically educated the elite: there is discussion to be had on legacy admissions and paper-mill research groups that pad the resumes of high school applicants with research of little merit.