I'm currently trying to decide where I want to apply for math grad school. Many of my professors recommended places that were not as selective as the top grad schools but still had what they thought were strong programs in the field I want to go into (algebra). I was wondering whether going to a school that's not as selective will hurt my ability to get a job in academia in a top/very good university. A friend of mine told me that what happens is that since the PhDs from the very best math programs can't get job offers where they went, they will end up landing research positions at the very good (but not top) universities. Then those who got their PhDs from very good (but not top) universities will get the jobs at the OK universities, and things will sort of go down from there. Is there any truth to that? At first you might be thinking, Why does it matter to him? If he wants a PhD he should go wherever he gets in. But what it boils down to for me is that I would like to go to grad school right after I graduate, but I think my chances of getting into the very strong programs will be better if I wait a year.