Is it possible to get another math PhD 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?
 A: I agree with item 2 of Alexandre Eremenko's answer. Lower tier departments who care more about how they appear to the dean rather than the actual quality of the research do sometimes go after Ph.D.'s from top schools because it looks better. But departments that have actual aspirations of having strong research will look at anyone who has a strong track record, regardless of where that person got a Ph.D.
Here are some thoughts:
1) Get to know as many strong senior mathematicians as possible, especially those who work in your field or closely related ones. Try to make sure they are familiar with your work by giving seminars at their schools, attending and giving talks at conferences, posting your papers on arxiv, and sending a PDF of your paper to people you think might be interested (but don't overdo this).
These people are invaluable in at least two ways: 1) Putting in a good word for you, whether in a formal letter or informally by email or phone. 2) Providing useful guidance to you on which departments are hiring and where you stand the best chance.
Who writes strong letters for you matters at least as much as where you got a Ph.D.
2) When visiting a department that you think you have a shot at getting a job at, don't be afraid to ask them what the prospects are and what they are looking for. Getting a better sense of how each department chooses how to hire is invaluable.
3) Maintain good and friendly relations with absolutely everyone in your field. For example, when you write a paper, cite people generously, including anyone who has done anything related to your work, whether you used the work or not in your paper. Showing your appreciation for others' work by citing them is a good way to build a lot of goodwill.
A: *

*I suppose that if you want a second PhD in Math you have to hide the fact that you already have one.
But I do not recommend you to do this. What will you do with your existing publications ?
In my university at least, it is a policy not to accept to the 
PhD program those who already have a PhD.
(I don't know whether this policy is written or unwritten. And how strict it is. Probably they do not
ask explicitly.
And I know people who actually had a PhD (in another country) and who were accepted to our PhD
program. They did not mention in their CV that they had a PhD.  

*It is probably true that most people employed by the "second-tier" math departments are from
"top" universities. But it is not true that the hiring committees do not consider other applications.
I know many people in "top" universities who have PhD from little-known places. 
