Dedicated to Johanna
There are two observations about women in physics and mathematics that are at odds with each other. The first is that there are relatively few women in science. In a typical seminar or conference presentation I have counted that just over ten percent of the audience is female. The second is that, despite the relatively few women, they are by no means second-rate scholars. The first person to ever win two Nobel Prizes was a woman–Marie Curie (1867–1924). But I do not have to go far-far away and long-long ago to find first rate women scientists. I just have to go down the corridor, well actually down the corridor and up a flight of stairs since my office is in the ground floor administrative ghetto while the real work gets done on the second floor. Since women are demonstratively capable, why are there so few of them in the mathematical sciences?
A cynic could say they are too bright to waste their time on such dead end fields but as a physicist I could never admit the validity of that premise. So why are there so few women in physics and mathematics? It is certainly true that in the past these subjects were considered too hard or inappropriate for women. Despite her accomplishments and two Nobel prizes, Madam Curie was never elected to the French Academy of Sciences. Since she was Polish as well as a woman the reason may have been as much due to xenophobia as misogyny.
Another interesting example of a successful woman scientist is Caroline Herschel (1750–1848). While not as famous as her brother William (1738–1822), she still made important discoveries in astronomy including eight comets and three nebulae. The comment from Wikipedia is in many ways typical: Caroline was struck with typhus, which stunted her growth and she never grew past four foot three. Due to this deformation, her family assumed that she would never marry and that it was best for her to remain a house servant. Instead she became a significant astronomer in collaboration with William. Not attractive enough to marry and not wanting to be a servant she made lasting contributions to astronomy. If she had been considered beautiful we would probably never have heard of her! Sad.
Sophie Germain (1776–1831) is another interesting example. She overcame family opposition to study mathematics. Not being allowed to attend the lectures of Joseph Lagrange (1736–1813) she obtained copies of his lecture notes from other students and submitted assignments under an assumed male name. Lagrange, to his credit, became her mentor when he found out that the outstanding student was a woman. She also used a pseudonym in her correspondence with Carl Gauss (1777–1855). After her death, Gauss made the comment: [Germain] proved to the world that even a woman can accomplish something worthwhile in the most rigorous and abstract of the sciences and for that reason would well have deserved an honorary degree. High praise from someone like Gauss, but why: even a woman? It reminds one of the quote from Voltaire (1694–1778) regarding the mathematician Émilie du Châtelet (1706–1749): a great man whose only fault was being a woman. Fault? And so it goes. Even outstanding women are not allowed to stand on their own merits but are denigrated for being women.
But what about today, does this negative perception still continue? While I have observed that roughly ten percent of attendees at physics lectures tend to be female, the distribution is not uniform. There tend to be more women from countries like Italy and France. I once asked a German colleague if she thought Marie Curie as a role model played a role in the larger (or is that less small) number of female physicists from those counties. She said no, that it was more to do with physics not being as prestigious in those counties. Cynical but probably true; through prejudice and convention women are delegated to roles of less prestige rather than those reflecting their interests and abilities.
My mother is probably an example of that. The only outlet she had for her mathematical ability was tutoring hers and the neighbour’s children, and filling out the family income tax forms. From my vantage point, she was probably as good at mathematics as many of my colleagues. One wonders how far she could have gone given the opportunity, a B. Sc., a Ph. D? One will never know. The social conventions and financial considerations made it impossible. Her sisters became school teachers while she married a small time farmer and raised five children. It is a good thing she did because otherwise I would not exist.
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 A fellow graduate student who died many years ago of breast cancer.
 Probably the greatest mathematician that ever existed.