TITLE: Does it ever make sense NOT to go to the most prestigious graduate school you can get into?
QUESTION [64 upvotes]: I'm a senior undergrad at a top-ish(say, top 15) math school. I'm a solid, not stellar, student. This year I'm taking the qualifying exam grad courses in algebra and analysis and have been taken aback by the "pressure cooker" atmosphere among grad students here. That is, even moreso than in the undergraduate program.
If I'm self driven, could going to a "less prestigious" school afford me more space(I mean in a psychological sense) to produce a more solid contribution to math? By "less prestigious", I mean a school "ranked" significantly lower than the range of schools that I could comfortably get into. For me, "less prestigious" would be ranked around 40-60 on, say, USNews or NRC.
My reasoning is that at such a school, I would be more able to learn the fundamentals at my own pace, as opposed to a pace dictated to me by the program. I know I want to do math, and I think my learning style may be better suited to going at my own pace. Thoughts?

REPLY [4 votes]: There aren't anywhere near enough faculty positions for all the PhDs we churn out, not even close.  Academia might dramatically contract over the next couple decates even.
Industry knows almost nothing about your PhD subject, but they recruit heavily amongst the Ivy league graduates.  Also, one finds vastly more parochialism amongst the smaller schools.
Imho, you should select the best school possible because (a) it'll make you a broader more flexible mathematician and (b) it'll maximize your chances of doing the most interesting mathematics you can if/when you leave academia for industry. 
You should however realize that school rankings aren't the entire story.  There are schools that seriously over work their teaching assistants, like Purdue for example.  Avoid such places even if it costs you institutional prestige.