My undergrad being in a field other than mathematics (and not in the US), I couldn't get into the Princeton/Harvard/MIT tier of universities for my math PhD. I settled for a lesser program and got my PhD. I did land a postdoc at a half decent institution, but 4 years later, I can't even get search committees to look at my TT applications. I am no genius, but I don't think my publication list is that uncompetitive.
So I have two questions:
Do search committees not want to put a blot in their faculty list by interviewing/taking applicants who don't have Harvard/Princeton (and similar) etc on their CVs?
Is it possible to completely re-do my PhD? I mean, can I apply simply to math PhD programs again? Do I stand a chance at the top tier universities, especially since I am still below 30? I know extremely well that a PhD from Princeton/Stanford etc is not guarantee of a TT position, but it obviously improves the odds. And if I apply to PhD programs, should I hide the fact that I already have a math PhD?