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For courses like Math, English and Econ, there's usually a strong correlation between generally the top schools and the top schools for your major. There are exceptions of course (e.g. going to Caltech for English) but you get what I mean. You're generally safe with a math major from any top-tier school. What's more important for your prospects is doing well once you get there.
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Not really. To an outsider it may seem that math is a very straightforward major, but it isn't at all past MVC/LA/ODEs, and there are wide disparities between the top schools at the higher level. And since the best students will matriculate having already taken MVC/LA/ODEs, the fact that the top schools are all about equal quality at this level is irrelevant.
Princeton, Harvard, MIT, Berkeley,and Chicago make up the big 5, at least for graduate school. Undergrad is a bit harder to measure. For undergrad, I would add in Swarthmore as another school that produces many high-quality mathematicians, as well as Harvey Mudd.