Can I payoff student-loan debts working as a professor after getting a Ph.D. in mathematics?
Since nobody else has offered a direct answer to the title question...


  Should I take on debt in order to get a Ph.D. in mathematics?


Absolutely not.

If a PhD program isn't willing to waive your tuition and offer you a stipend (in the form of an assistantship or fellowship), they don't really want you.  Go somewhere else.  If they decide not to give you more funding after a semester or two, you're done.  Go somewhere else.