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<p>This is a pretty big claim to make, but I can’t say that I disbelieve it actually, even though I have never seen the course material taught in a Chicago course (but have seen the material taught at all the other schools mentioned). Know why? There’s this one professor at my school who is exceptionally famous, and comes from Chicago graduate school originally – the man’s classes always end up being FANTASTICALLY difficult, and students drop out of it rapidly. Also, interestingly his are one of the few courses at that level which are heavily based on exams still, even if less than 70%. </p>
<p>Now, obviously the other schools all produce top caliber researchers too, and the question to ask yourself is if this kind of high pressure environment will help or hurt you. To give an idea, one of the young stars of my school went to Harvard as an undergraduate and did NOT take Math 55, and the kinds of stuff he works on today is utterly crazy. Hard classes are great, but you shouldn’t take them at the expense of starting to grow discouraged with math, because in the end, research is research, and it’s clear that going through the hardest classes isn’t necessarily the way to become the best researcher. It depends what teaches you the most.</p>