"not enough data to be statistically significant"

^suspect this is incorrect.

I am well aware of the quality of the schools in Iran and can directly compare it US schools, having gone to school in both countries. That Newsweek article is not surprising to me, but in some areas it is inaccurate in my opinion. You do see high quality individuals graduating from Sharif university, which is highlighted in the article, but concluding the school itself is "successful" or competitive is incorrect. The fact of the matter is that there is a nationwide exam to enter college level education for all schools and you basically choose your school (and major) based on your rank in that exam. In that society, engineering majors, specifically Electrical Engineering majors, tend to have high status, so if you do well, you end up going to study EE at Sharif University, probably not because you are a fan of EE or you think Sharif is any good: it just has to be better than other schools.

The outcome of this is simple: you'll have selected top N individuals from an exam of half a million people and put them in a single school. Of course you're going to see those people shine. That says _nothing_ about the absolute quality of what that school gives you, just how good it is relative to its peers in the country, and I define quality as "output - input". The "input" is high quality, but the delta is merely meh in my opinion. Also, the students are high quality--the faculty are generally not (unlike what's mentioned in the article), but they do end up taking some credit.

In terms of the contribution of the country, I can just say that she is a survivor of an accident years ago, where seven talented math students died, whom had similar achievements to hers at the time. Overall, the contribution of the country to its mathematicians has been negative, specifically so to the female ones.

I want to second the sentiment that national investment supports achievement like this. IMPA has been very important for Brazilian mathematics, bringing people from across the world to Brazil to do high-level research. This means that some Brazilians who don't have have the opportunity or desire to move to Germany or California or Korea can work with and learn from amazing mathematicians who come to them, in Brazil.

Since 1990, at least one Fields Medal winner has worked in France -- until this year. France has a culture of supporting mathematics and mathematicians. It has its quirks and difficulties, but national support for research has played an important role.