About pre-reqs: third and fourth year PureMath classes at UofWaterloo consisted of math I already took in HighSchool in Romania: group theory, ring theory. Plus some calculus I already read in high school out of curiosity: measure theory and the Lebesgue integral. Another Romanian guy at UofW was auditing 4th year classes while in his first year (he is now a math professor at an American university)

I can see a committed and gifted student being able to get most of the pre-reqs for doctoral studies in America or Canada while in high school.