I don't really have energy to talk extensively, but I gotta say, mathematics is a painful field to go in as a woman.
Where I come from, anyway, as an undergraduate.
All your teachers are men. Every graduate you meet will be male. Some of them will make jibes at you for being female. You can never tell when they're complimenting you and when they're messing with you.
All the people who wrote every single theorem you learned were men. Period.
You don't have to walk two inches on the internet to find someone explaining that women just really aren't as good. Period. By very smart people, on very legitimate sites.
You have female celebrities writing books like this to great acclaim, bringing mathematics to the young women who clearly wouldn't get it if it weren't all about dates, pink, and parties. Oh, and above all, boys.
For me, at least, I can never tell if I'm doing well or just being another uppity female who thinks she can do math and doesn't really get it. The stress is murderous. During the school year, I often get a stomach ache that never really goes away.
If you say you're worried about getting into graduate school, everyone will tell you "it's okay. You'll get in. You're a girl," so that no matter how well you do, it will never be your work. Men usually get to say "It was because I worked hard." They don't have to confront their privilege. But yours is obvious and unfair.
I often have to remind myself that I don't want to date or get married or have children, because statistically those are characteristics of women who don't go far in mathematics. If you're a woman and want a family, you'd better not do math, is what the brochures say, all those articles to explain why you won't get very far in life. Here are the traps of being a woman, piled with all the traps of being a person that men can fall into. Better'd watch out. You don't take enough risks because you're a woman. You don't study as hard because you're a woman. You don't focus as well because you're a woman. You waste your time on stupid shit because you're a woman. You pay attention to your appearance because you're a woman. You're bad at math because you're a woman. You're going to make it only because you're a woman and they feel bad about not having even numbers or some shit, these folks are too PC, aren't they.
For me, at least, I end up being ashamed of being female and wishing that I had just had the good fortune to be born male, so that I could do this and enter in a society of my people. Instead, I feel like I'm worming my way into somewhere I don't belong. A society of men, where my only recourse is to be the absolute top at all times, in everything. The best in understanding the social hierarchy. The most enthusiastic. The one with the clearest proofs. The one with the best ideas. The one with the most confidence. And otherwise, I won't make it anywhere.
Because claims of pseudointellectualism or not, appearances do matter. I've already made the mistake of wearing a woman's face and a woman's body while trying to do math. It's something I have to actively work to negate.
I second basically everything Vector said, and throw in my own screwy situation. I sort of can see it from both sides, because that's more or less where I am.
We are all trapped by social expectations. One who does not humor society's expectations will be disapproved of by it, which will make success difficult if not impossible. This applies at infancy/childhood, continues into adulthood and sustains until we die. Pressure, from not conforming to societal expectations, can come from overt, internal, and systematic sources. All of this negatively, and as a rule needlessly, effects the individual.
Beginning at childhood, we have social expectations that grow as our social circle grows, beginning with parents and expanding to relatives, friends, teachers, etc. Schools and care taking functionaries will divide children by sex. The division itself, without hard barriers, limits our peer groups and from there what we are directly exposed to in frequency and proximity. Failure to conform to whatever society expects of children will result in their not being included at some point. This applies to both genders and to other characteristics of the child, from intelligence, athleticism, charisma, maturity, and economic status, to many others.
Once one grows older, the pressure is not only social but economic. If one does not met society's expectations, being hired, much less maintaining a job is difficult. Appearance and social connections win out over merit and ability, provided the bare minimum of standards for ability is met. Age does not lessen these rules or their application but might provide some respite if the person is truly, ever so rarely, self sufficient (doesn't even need a job).
As applied to me, as a transsexual woman forced to live a lie, I can see both sides. Again the rule of deviating from society's expectations = punishment, applies. Here, I fake what I must to make society think I meet its expectations. If I were to show up to work as I actually am, while providing the same service, information and results to my boss and his clients, I would be summarily fired. (there is no legal recourse by the way). Without belaboring the point more than required, one would think if your lawyer knew what the hell he was talking about would be more important than appearance given you risk prison time or paying a large monetary judgment if he or she does not.
My story is not unique, though it is a bit of a twist. What if you are a "masculine presenting," "tomboyish," or simply not overly "girly" woman who is perfectly happy being a female but does not restrict yourself to the standard societal expectations. The same applies to a male who is "effeminate presenting," (There really isn't a non insulting term for a male counterpart to a tomboy and that says something), or simply not "macho" man (and heaven help you if you're gay in the US). All of the above people are perfectly understandably feeling pressured by society to change, and there is no reason for this. Any two characteristics can be substituted for gender/sex in this example, the logical framework, holds true.
Speaking as close to "objectively" as I can, not a damn bit of this should matter, at all. The question should be, can they do the work in question.
This is of course, an oversimplification. I'm capable of witting a book but not cruel enough to expect you to read it.