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.
Here is the statement from the Graduate Division at Berkeley:
Duplication of Degree.
Students who already hold a doctoral level degree are not admitted and duplication of degree or admission to a lesser degree is not permitted. However, in extraordinary circumstances, the faculty of the department may request an exception from the Dean of the Graduate Division. The department must demonstrate that the second degree field of study and program are distinctly different from that of the original degree, and that there is a professional or scholarly purpose that requires this second degree.
Similar restrictions apply throughout the UC system. Harvard likewise states:
Persons holding a PhD or its equivalent, or who have completed most of the work required to earn the PhD elsewhere, may apply to a PhD program in the Graduate School only if it is an unrelated field of study.
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.