Friday Bookshelf: Triangulating Women in Math

Three for the price of one in this week's Friday Bookshelf! Which maybe makes up a little for the complete lack of a Friday Bookshelf last week.

First up is Lynn M. Osen's classic, originally published in 1974 and simply titled Women in Mathematics. Osen's slim volume has been beloved - and in print - for over thirty years for the biographical sketches of eight prominent women mathematicians: Hypatia, Maria Agnesi, Emilie de Breteuil, Caroline Herschel, Sophie Germain, Mary Fairfax Somerville, Sonya Kovalevsky, and Emmy Noether. The last chapter, titled "The Feminine Mathtique", is still depressingly apt in many ways, though we may rejoice that formal quotas are no longer in place for women's admission to mathematics programs.

Next we take a look at Margaret A. M. Murray's Women Becoming Mathematicians: Creating a Professional Identity in Post-World War II America. Murray is herself a mathematician and gives an intimate look at the lives of women mathematicians in the post-war years. A special pleasure of this book is inclusion of photographs of many of the interview subjects. Drawing on oral history interviews with 36 women PhD mathematicians, Murray considers family background, high school, college, and graduate school experiences, and the intersection of career and life. She also examines the question of professional identity in light of the prevailing mythos, exemplified by a quotation from Paul R. Halmos: "[Y]ou have to be born right, you must continually strive to become perfect, you must love mathematics more than anything else, you must work at it hard and without stop, and you must never give up." For the women in Murray's study, becoming a mathematician meant something else; it meant balancing two conflicting cultures, "the lower-status, female-identified culture of teaching, and the higher-status, masculine culture of research. For some, this meant identifying exclusively [with one]...for others, it meant striking a compromise...for a small minority, [it] meant moving beyond the narrow categories...into new areas of creative activity."

Imagine being one of 10 women a year to earn a PhD in mathematics, in the years between 1940-1959. That's 10 women a year in the whole entire U.S. of A. What trials must one overcome, what tribulations must one endure, on the pathway to that degree? Here's what Alice Shafer had to say about her undergraduate years at the University of Richmond:

In my junior year of college, the dean of women called me into her office and said that the head of the mathematics department was flunking all the women mathematics students, for he wanted no women majors in mathematics. The dean told me, "You are to stand your ground." I was too naive for it to have occurred to me not to stand my ground!

The course the department head was teaching must have been an advanced calculus course. A woman in my class who was a chemistry major had not been flunked - as she told me later - but had been given a D. I believe that earlier she had been thinking about being a mathematics major. Our examinations were not returned to us, and we were never allowed to see them. But a member of the history department told me that the mathematics department head had said in a faculty meeting that I had made 100 on my final examination, and she was shocked when I knew nothing about this.

Schafer was so damn brilliant that eventually the Moron Department Head had to concede that she was capable of doing mathematics, especially when she won a prize for best performance by a junior on a competitive exam. "I never thought you would win the prize" was his grudging acknowledgement, which left her seething with anger for years. Having to expend emotional energy on Moron Management is something the boys just never had to contend with.

Murray discusses, in her introduction, "The Myth" of the mathematical life course, which she notes is similar in many respects to the ideal of any academic career - early identification of talent, single-minded dedication, uninterrupted progress - oh hell, it's just how a man's life is supposed to unfold. Unfold, while a woman sits quietly in the background tending to the homefire and the little ones.

If you've had enough mathematical myths to last you a lifetime, then Claudia Henrion's book is the one for you: Women in Mathematics: The Addition of Difference. Henrion, like Murray a mathematician, also interviewed other women mathematicians. However, her goals were to examine and expose prevailing ideologies that govern mathematics culture, and to consider how these ideologies affect the lives of women doing mathematics. The book is organized into separate sections each dealing with a different "mathematical myth", paired with relevant interviews or summaries of interviews. The myths that Henrion tackles are as follows:

• Mathematicians work in complete isolation
• Women and mathematics don't mix
• Mathematicians do their best work in their youth
• Mathematics and politics don't mix
• Only white males do mathematics
• Mathematics is a realm of complete objectivity

Henrion translates these into great titles for her chapters. For example, Myth #1 becomes Chapter 1, Rugged Individualism and the Mathematical Marlboro Man. Hee!

In Chapter 3, Is Mathematics a Young Man's Game, Henrion writes "While I had questioned that mathematics was a young man's game, it had not occurred to me to question that mathematics was a young man's game." So off she goes to examine the evidence, which lo and behold shows that mathematicians are not less productive, nor do they produce work of lesser quality, when they are older than they do in their youth. And the women she interviewed felt strongly that the best work they had done had come later in life; one woman said she had "a new kind of pleasure" in doing mathematics now that she was older and understood more mathematics, more of the field, and could make more connections between ideas. But the assumption that one's best work is done in youth remains, and is harmful to women especially. It's built structurally into mathematics, such as in the Field prize having an age limit of forty - forty! Imagine! I'm sorry kids, but forty is when a woman is just beginning to hit her stride!

The Myth of Youthful Productivity certainly does not allow for someone to devote a little time to childrearing, or even to just having a life. Having a life? That's for when you're old and dried up and incapable of mathematics!

This is such a dumb myth. Of all fields, mathematics ought to be the most hospitable to women. It requires little funding, little in the way of equipment. You can work on mathematics virtually anywhere (though as the example of the University of Wisconsin seems to illustrate in Henrion's book, a diverse circle of supportive colleagues is certainly a good thing to have) and at pretty much anytime. You aren't tied to a lab bench, or changing samples at a certain time; you aren't dependent on some large piece of equipment that only a few universities have; and the data shows that you can be productive throughout your life, so having kids shouldn't be any hindrance.

And furthermore, this is a myth that does not benefit men in any way that I can see. Why do they cling to it so? Why do they want to believe that they become washed up and useless after age 40? Why do we venerate youth so? This is just dumb. I mean, I know young bodies are hot, but why have

(Hot Young Body) = (Must Be Capable of Producing Really Great Mathematics)
and

(Edging Towards Age 35) = (Suddenly Incapable of Any Decent Mathematics)

become a mathematician's favorite equations?

Well, you will find much to think about in Henrion's book, and you will certainly enjoy learning more about the women she interviewed. All three of these books are easy and compelling reads, and would make a good addition to anyone's bookshelf (even if it's just your TBR bookshelf. :) )

Two books on woman and mathematics that I recently learned about but do not own, haven't seen, can't really tell you anything about, but thought I should just mention here, are the following:

Change is Possible: Stories of Women and Minorities in Mathematics by Patricia Clark Kenschaft, another mathematician.

and

Complexities: Women in Mathematics by Bettye Anne Case.

From Change is Possible, here's the first paragraph:

"We hired a woman in our department fifty years ago, but her students had trouble getting jobs. I don't see why we should make that mistake again!" So said a leading retired mathematician at the business meeting of the American Mathematical Society in January 1990. By then, it was shocking to hear such sentiments expressed publicly, but apparently he felt he could say it - and he clearly believed it.

From what I read of the introduction on Amazon, this looks like it could be a very good book.

Complexities appears to be a combination of biography, history, opinion, and research. Hard to tell without seeing the book itself whether that mix is successful or ends up just being a mish-mash. But, if you are desirous of collecting stories of women mathematicians, this would probably expand your library.