Of course, one has the best chances of becoming a professor if able to get into Princeton, Harvard, MIT, Stanford, Chicago, and Berkeley.
But it is unlikely for most to get in. The next tier of Ivys or places like UCLA have a smaller but still passable chance in academia. What about schools in the next range, or even outside that? I'm thinking of places like
UIUC
UMD
UCSD
UW Madison
UMN- Twin Cities
JHU
Are these schools ranked too low to have a passable chance?
Can you still have a math career after attending these schools?
Re: Can you still have a math career after attending these schools?
Not at all. The links below give the post-PhD placement of people who went to UMD, JHU, and UC Davis (not from your list, but "ranked only slightly below" the others).Are these schools ranked too low to have a passable chance?
https://www-math.umd.edu/graduate/prosp ... atics.html
https://mathematics.jhu.edu/graduate/placement/
https://www.math.ucdavis.edu/grad/degrees_award