Most successful women in mathematics have male relatives who already have math PhDs, in my experience. That is, they have someone to talk to about math, because through middle school and high school the boys won't talk to them unless they're fawning (not fucking kidding about this). It's very hard to learn any math when the more successful you are, the smaller the pool of people to discuss your notions with is. It's also very hard when in order to talk to someone, you're expected to humiliate yourself and make yourself look as small and harmless as possible. When you get to college, you won't have that problem, but folks will be *shocked* if you're marginally competent.
Add to that all of the "scientific" "research" trying to explain to you just why little old you can work as hard as you want, but you'll never succeed. The goalposts always move. If the average woman is just as capable as the average man at math, then they'll start saying that the problem is that you have to be really
above average, and there just aren't any women who can do that. Whatever problem you have, they'll blame it on you. Never mind the great female mathematicians of yesteryear, and never mind the talented women today, and never mind that women pioneered the very closely related field of computer science. You're a girl. You're incapable. Studying math is a waste of your life, because you'll never, ever make it. So why not go have babies?
Remember that story about a woman who was denied tenure and is still being questioned 15 years later as to her right to teach? The undergraduates pass this story around between them. The women get the message that they'd better sit down and shut up until they're being considered for tenure, because before that any complaint of sexism will ruin their career chances with all the rumor-mongering.
There's also knowledge that being a woman means you will be seen less successful than a man with the same credentials. So I might as well have a B- average.
More than that, I guess, is the information constantly being sent my way that everything is my fault. I am smart. I am talented. And fuck it, I am
really good at math. I'm consistently the sharpest person in the room. I solve problems six times faster than the average Berkeley undergraduate, and if I were anyone else I'd probably be getting preferential treatment and deference. In male math students, being bad at computation is a sign of exceptional genius. For female math students, being bad at anything is considered a sign of being unexpectedly stupid.
How prevalent is the next question there.
Very. Prevalent enough that the American Mathematical Society pioneered a global study in gender differences in mathematics, correlated to local stereotypes about who was better (in Arab countries, the stereotype is that women are better). Unsurprisingly, taken globally there was no difference in skill and disparities followed stereotype locally. This is... a big deal. Mathematicians generally just want to stick to mathematics.
Out of curiosity, are confiding's on gender roles and the likes ever a part of any of your male and female relationships, particularly the less closely attached ones? How much?
I've learned that it's generally not a good idea to talk to people about it, especially when you don't know them all that well. Folks have, for example, tried to convince me that people think I'm stupid because I'm ugly, not because I'm female (while interrupting me to the point where I couldn't get a string of six words out). Or laughed about how of course more women should go into math, because lots of mathematicians still need wives.
To be honest, I have very few female friends (that's the math track for you!). In general, I've found it's safest to talk to Gender and Women's Studies or History majors, but there's a couple of math dudes who are okay. What I'm trying to say is, those are the ones I'd probably be able to speak to without thinking about it.
For that matter, how prevalent are (in the general populace) the relationships themselves? It's appears to be a rarity to have anywhere near the number of close-knit friends of your gender with the other.
No idea, but again--almost all of my friends, close and otherwise, are men. I have two close female friends and have a lot of female not-so-close friends, who would probably be supportive but wouldn't... I dunno,
get it.