It is my privilege to know (just a little) the first United States woman to gain a gold medal at the IMO. I know her mother much better and discuss mathematics education with her online frequently. In all countries, it takes a really sound elementary education in math to gain a chance at qualifying, through repeated rounds of testing that winnow down a national population, for a national team to the IMO. Most of the United States young people I know who have made it onto the United States IMO team have been deeply involved in mathematics competitions at younger age levels for many years, and the young woman whose mother I know was no exception. She was homeschooled for her primary and secondary education. East Asian countries and some eastern European countries seem culturally (compared to the United States) to have much less of a presupposition than many Americans have that girls will not do well in math, and correspondingly more girls in those places do well in math because they stay involved in math.
