Can we get a PhD in mathematics without publishing?
It is typical in the U.S. that mathematics Ph.D. students do not publish anything at all prior to earning a Ph.D., I think even at the elite places. Publication per se is not such a high priority, nor over-literal gauge of accomplishment, as it seems to be in some CompSci and Engineering disciplines (at least in the minds of some people).

That is, to be clear, especially for people who've thought, or been indoctrinated to think, that the measure of the value of something is the prestige of the conference or journal or ... in which it was published, the idea in mathematics still does seem to be that the thesis advisor and thesis committee decide whether the candidate has done sufficient work to earn the degree.

Seems a sane system to me, especially given the acceleration of freneticism elsewhere.