If one gets a phd in math, is it able to be admitted to another phd program in math? It is not for me, for someone else.
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Here is the statement from the Graduate Division at Berkeley:
Similar restrictions apply throughout the UC system. Harvard likewise states:
I know that at least until the late 1990's MIT's Computer Science Department had a rule that nobody with a Ph.D. (in any field) would be admitted to their Ph.D. program; the rule was changed in the early 2000s so that a Ph.D. in a field other than Computer Science was no longer a bar for admission, but it still placed applicants at a disadvantage. I would expect similar rules to exist in other Departments at MIT, but I did not spot any explicit rule in the mathematics admission page.
Similar policies are explicit in many US universities; even in those where it is not explicit, space limitations will usually lead admission committees to consider such applications very skeptically, prefering to give spots to new students, and if they are very keen on the applicant, will likely suggest a post-doc instead.