In terms of research, how do organizations like the US News World report compare math departments from US universities? Do they look at the range of mathematical research and the depth? Do they look at how prestigious a journal professors have published in?
closed as off topic by J. M. is a poor mathematician, t.b., user940, Qiaochu Yuan Jul 24 '11 at 5:24
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They rely very heavily on peer review and assessment. Here are two sources (with lots of overlap) on the matter -
This makes it even more difficult to say what really matters. What makes a group of mathematicians respect one university over another? There are many different possibilities. In all likelihood, there's a lot of handwaving.