Alice T Schafer is chair of the mathematics department at Marymount University in Arlington, Virginia.
The 1989 National Research Council report, ``Everybody Counts,'' says (page 23) that, ``gender differences in mathematics performance are predominantly due to the accumulated effect of sex-role stereotypes in family, school, and society.'' Of course, such a statement would not have been surprising had it appeared in the AWM Newsletter--women have been saying this for years. But it was refreshing to see it in such a report. The report also quotes Workforce 2000 (page 18) as saying, ``White males, thought of only a generation ago as the mainstays of the economy, will comprise only 15% of the net additions to the labor force between 1985 and 2000.'' The report identifies women as one group that will be needed to fill a gap left by the absence of white males. What is being done to welcome women into mathematics and keep them there?
Some of the statistics are, unfortunately, depressingly familiar. According to Science magazine (28 June 1991, page 1781), there are 303 faculty in the ``top ten'' mathematics departments (identified as Berkeley, Caltech, Chicago, Columbia, Harvard, MIT, Michigan, Princeton, Stanford, and Yale), and the women can be counted on one hand. One is Joan Birman, who is actually tenured at Barnard College, a women's college of Columbia University. Another is Sun-Yung Alice Chang, who was offered a tenured professorship at Berkeley, but is currently at UCLA. The third is Berit Stensones, who has been appointed to an associate professorship with tenure at Michigan. And the fourth is Marina Ratner, who is tenured at Berkeley; for a history of her original appointment, see the AWM Newsletter from 1974 and 1975. The situation among non-tenured faculty is equally dismal: one woman out of eighty-six.
According to the October 1990 issue of Notices, there were 991 doctorates awarded in mathematics by institutions in the U.S. and Canada in 1989-1990, 18% of which were awarded to women. From that crop of doctorates, the thirty nine ``Group I'' institutions employed 101 men, but just twelve women. Such statistics are often explained away by saying that there are no qualified women ``out there.'' This is difficult to believe when one looks at the percentage of women receiving doctorates in mathematics, which has been plus or minus 20% for nearly 10 years now (with many of them coming from the ``top ten''). And in recent years, many women have received postdoctoral fellowships in mathematics and have been invited speakers at national and international research conferences.
Once I had a conversation with a male mathematician who said he would never hire a woman mathematician because she would probably sue if she were not granted tenure. I know of no woman mathematician who has ever advocated that a woman be appointed to a position for which she was not qualified or that, once appointed, she be judged on any basis different from that of a male member of the department. Indeed, I was once asked by a man at one of the ``top ten'' institutions what I would do if faced with the following situation he encountered in his own department. A man and a woman were being considered for promotion to full professor. The woman's research was inferior to that of the man, but some members of the department felt that if one were promoted, the other should be also, for personal reasons. My answer was absolutely not! The woman's research should be judged on the same basis as any man's in the department. I suspected that my answer was a disappointment to the man who asked me; I think he had expected me to say that the woman should be promoted despite inferior research.
On a different occasion, when I was talking to a mathematician at another of the ``top ten,'' I asked why there were no women on the faculty. His answer was that if the department could find anyone as good as ``X,'' a woman at a less prestigious university, that his department would hire her. ``What about hiring X?'' I asked. No response--end of conversation. An answer I have heard many times from men at research universities is that women have children and cease to do research, but there are so many counterexamples that the argument is fallacious. And anyway, how many men, with or without children, have short ``research lives''?
There has been a great deal of discussion in recent years about attracting more students--and, in particular, more women--into graduate school in mathematics. Programs and funding are not enough. There must be women on the faculties, and the women students must see their work evaluated on the same basis as that of their male colleagues. When it comes to mathematics, male and female students should be treated the same. But when it comes to certain kinds of social factors, it is, unfortunately from my viewpoint, sometimes necessary to treat women differently. During my years teaching undergraduates, I told my female students that I would not write a letter of recommendation for them for entry to graduate school unless they promised to complete the work for the doctorate. I do not tell my male students this, and some of them did not complete the work for the doctorate. One of my Wellesley students now jokingly tells me that the reason she has a Ph.D. is that I had refused to write a recommendation for a National Science Foundation (NSF) fellowship unless she promised she would complete the work. She is now married, has children, and does research.
It has been well documented that many capable girls and women have reacted to the myth that females cannot do mathematics by avoiding mathematics courses and steering clear of careers in mathematics and science. If schools, colleges, and universities have failed here, women and some men have worked to eradicate this injustice and have established organizations and programs for this purpose. There is space here to mention only a few.
I believe that by now all mathematicians know of the existence of the Association for Women in Mathematics (AWM) founded in 1971 as an independent organization and with offices at Wellesley College since 1973. A history of AWM, written by former AWM President Lenore Blum, appears in this issue of Notices.
Two years after AWM was founded, due to the efforts of Cathleen S. Morawetz, aided by Isadore M. Singer, the AMS created the Committee on Women in Mathematics, with Morawetz as its first chair. Under her direction, a Directory of Women in Mathematics was published in order to show the mathematical community that there were women who were qualified to be faculty members at research institutions, to be speakers at mathematics meetings and research conferences, and to be appointed members of important national committees. During my tenure as the third chair of the Committee, a second Directory of Women was published, and I. N. Herstein, a member of the Committee, wrote an article in Notices, ``Graduate Schools of Origin of Female Ph.D.s'' (April 1976, page 166). His idea was that, if women preparing for graduate school in mathematics were aware of the departments which had in the past been hospitable to women, they might want to consider those schools. At that time, the Committee also submitted several proposals to the NSF for funding for programs that would benefit women mathematicians, but, unfortunately, none of them was funded. (I am happy to say that in recent years the NSF has begun to fund programs almost identical to the ones the Committee recommended.)
The Committee was later expanded to the AMS-ASA-AWM-IMS-MAA-NCTM-SIAM Committee on Women in the Mathematical Sciences and is currently chaired by Susan Geller of Texas A&M University. Geller reports that the Committee has developed a questionnaire to be distributed at Ph.D.-granting institutions in an attempt to determine why students in the mathematical sciences leave graduate school. The questionnaire has already been tested at six cooperating institutions, and as soon as funding is available, the study will include all the Ph.D.-granting institutions. The Committee has also been collecting statistics on the relative acceptance rates of male and female authors in various journals. (Journal editors interested in this study should contact Geller.)
In 1975, the MAA established the Women and Mathematics Program (WAM), the first program in the country designed to encourage female students to continue to study mathematics and to seek careers in fields requiring the use of mathematical tools. WAM participants are women from business and industry whose career choices involved a strong background in mathematics and science. They serve as mentors, role models, career counselors, and classroom visitors to elementary, middle, and high school students in sixteen regions throughout the United States. Many of these WAM participants also arrange plant tours for groups of students. The current director of WAM, Alice Kelly of Santa Clara University, says, ``We work with both male and female students in our classroom visits, career counseling, and tours, thus exposing young males to the woman of today.''
Many colleges and universities have instituted programs to encourage girls in elementary school and to show them how exciting mathematics can be as well as instituting programs for high school women students. An excellent reference which has descriptions of many of these programs is the proceedings of the National Conference on Women in Mathematics and the Sciences, held in 1989 and organized by Sandra Z. Keith of St. Cloud University.
In 1987, the MAA established a second committee on women in mathematics, known as the Committee on the Participation of Women, chaired by Patricia Clark Kenschaft of Montclair State University. Among the Committee's recent endeavors is the MAA publication ``Winning Women into Mathematics,'' which includes a list of fifty-five cultural reasons why women are underrepresented in mathematics. During the national meetings in the past couple of years, the Committee has presented skits using mathematicians as actors to dramatize ``micro-inequities'' that have actually happened within the mathematical community. Kenschaft describes micro-inequities as ``small slights that are often humorous in themselves but chip away at women like water dropping on a rock.''
Charlene Morrow and her husband James are Directors of SummerMath at Mount Holyoke College. Describing the program, she writes: ``SummerMath, now in its tenth year, was designed to address the underrepresentation of women in mathematics-based fields. It is an intensive, six-week program for high school age females that provides new perspectives and new experiences in mathematics, computing, and science. We emphasize greater conceptual understanding, affirmation of young women as capable members of a learning community, and the importance of constructing one's own understanding of complex ideas ... . The atmosphere of the program is one of challenge with support: the challenge of rigorous study and hard problems with the support of a community of teachers, residential staff, and peers ... . Students learn to take charge of their mathematical education, gain a mathematical voice, and experience increased success in mathematics classes upon returning to school.''
The Sonia Kovalevsky High School Mathematics Days began in 1985. They were initiated by Pamela Coxson and Mary Beth Ruskai, who at the time held Office of Naval Research science fellowships at the Mary Bunting Institute of Radcliffe College. They suggested that the twenty-fifth anniversary of the Institute and the fifteenth anniversary of AWM be celebrated together, and the Sonia Kovalevsky Symposium was the result. As part of the Symposium, Coxson organized a Sonia Kovalevsky High School Day for high school women and their teachers in the Boston area. The Days have continued on a national scale with some funding from AWM and the remainder from local businesses and industries.
According to Donna Beers of Simmons College, the Sonia Kovalevsky Days held at her institution ``celebrate the beauty and uses of mathematics. The goal of these programs has been to show students women professionals working in attractive and challenging fields in which their mathematical preparation has proven indispensable. Above all, organizers aim to encourage young women to persevere in their study of mathematics throughout all four years of high school and beyond. The basic ingredients of these programs have included: hands-on workshops on cutting edge applications of mathematics, e.g. percolation theory, genetics, cryptology, chaos theory, and fractal geometry; career panel discussions led by women professionals, e.g. accountants, actuaries, aerospace engineers, statisticians, computer software engineers; and a lunch-time keynote speaker, often a woman scientist or mathematician who shares her mathematical biography, stressing the hard work required as well as the satisfaction and confidence that developing one's mathematical potential can bring. Student and teacher evaluations of the Sonia Kovalevsky High School Mathematics Days have been uniformly positive, urging that more be held more often, even at the middle school level in order to have a wider impact on young women students early on.''
As mentioned above, the NSF now funds programs similar to those first suggested in the early 1970s by the Committee on Women in Mathematics; for example, the Visiting Professorships for Women and the travel grants for women to attend professional meetings and conferences. The NSF also funds many other programs for women, such as research planning grants, Career Advancement Awards for experienced women scientists, and Faculty Awards for Women for those who are tenured but not yet full professors. The latter two programs aim to recognize the nation's most outstanding women scientists and engineers in academic careers of research and teaching and to retain these women in academia.
Another NSF program, Research Experiences for Undergraduates (REU), has proved to be of great value to women undergraduates. For example, the nomination papers for the AWM Schafer Prize, which recognizes outstanding undergraduate women mathematics majors, show that many of the nominees spent summers in REU programs, and some became coauthors of research papers. This past summer, the NSF funded a six-week Summer Mathematics Institute at Mills College in Oakland, California for twenty-four women students, who worked intensively on advanced topics in a seminar setting. The aim of the Institute was to encourage these talented students to go to graduate school in mathematics. For a more complete description of opportunities at NSF, consult the brochure ``Opportunities in the Mathematical Sciences,'' available from the NSF.
At present, fewer than one-fifth of the nation's mathematicians and scientists are women, and the prediction is that between 1991 and 2000 more than half of those entering the workforce will be women. We need to develop more ways of attracting and retaining women in mathematics. Women should be held to the same mathematical standards as men and should be judged on the same basis as men. Everybody Counts urges us to increase the pool of students who are successful in mathematics. Let's take that challenge seriously.