Men and the AWM

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About twenty years ago, some women used to say, “You can’t trust men over forty.” But this biased view was almost as bad as that of the men who blatantly declared, “Women can’t do mathematics.” Some remarkable men (now well over sixty) have supported women fully throughout the history of AWM. And many older men were oblivious rather than actively hostile—traditionally women had been perceived as less interested in mathematics and more involved with family than men, and some men were less aware of or affected by the aspirations of women.

As for today’s men under forty, they may not fully realize the harmful effects to women of past discrimination and discouragement and may not see that some still persists. Now that women are more accepted and more visible in the mathematics community, these younger men may acknowledge mathematical talent in women and may believe abstractly in equal treatment for all; but still they may not see that women have any disadvantage and, indeed, may feel that women receive extra advantages. They may feel threatened by women and worry that, with the extra competition, their own jobs are at stake. The ironic thing about this is that women also worry about seeing other women in positions that they are not qualified for; they feel that this will reflect badly on women in general. Studies quoted earlier demonstrate that women do not have an advantage in the job market. (See the Vitulli article cited above.) Nor is there any reason to believe that there are more unqualified women than unqualified men in choice positions. Possibly women are scrutinized more in these positions, by both women and men. Of course many of the new crop of younger male mathematicians have personal or professional attachments to women mathematicians or other women professionals; they may discuss these issues freely and see there are many more reasons to work together and support each other than to continue the battle of the sexes.

Some of the middle group of men (roughly ages forty to sixty) are philosophically allied with the older or the younger groups in attitudes toward women. A great number of them, however, are the chief champions of women; they not only realize the problems of women, but also work to assist women in their careers.

Many men have participated in AWM panels, contributed articles to the AWM Newsletter, and nominated women for AWM prizes (particularly the Schafer prize). Many male officers and employees of mathematical societies and government agencies have been extremely supportive of AWM activities. The Association encourages all groups to work together to solve real problems in the mathematical community; we all benefit from departments, panel discussions and committees with representation from both sexes and from many diverse groups. All will benefit from achieving a truly open exchange of ideas—free from assumptions concerning gender, ethnic, age or other such considerations—about mathematical research, about the education of our students, about mathematics in industry, and about advancing our profession.

Two Men Special to AWM. AWM is particularly indebted to Chandler Davis of the University of Toronto and Lee Lorch of York University for their support, advice and assistance with the advancement of the organization. By nature, both Davis and Lorch are gentle; but their resolve is strong, they believe deeply in equality and fair treatment for all, and neither will give up an argument about something they believe in. Both are now retired but not retiring! Some AWM members idolize them as “folk heroes”.

“While our founding mothers were creating AWM, twenty-one years ago, Chandler was at their side,” said the AWM message honoring Davis at his retirement party. The message goes on, “[Davis] was able to combine the work at MAG [Mathematics Action Group] with the support of AWM.…And his support has continued ever since. It has given all of us who have the joyous privilege of his counsel and criticism the opportunity to learn how one can be at the same time level-headed and uncompromising, patient and ardent, tolerant and unyielding” [ND92]. Davis’ own comments also were included in the article, showing his support and regard for the achievements of his wife¹, “Many years ago an older woman mathematician took me to task for spending so much time on housework so my wife could get her research done, to the detriment of my own career. I was flabbergasted: this wasn’t my own view of the relationship at all. It still isn’t.…It is true that I babysat and changed diapers and all; that was part of living my life the way I wanted to live it. My wife’s creative achievements…never were felt as representing a sacrifice; they were an important component in the satisfaction of my life” [ND92]. Davis still helps AWM in his quiet and dependable way, and it is still appreciated. For example, he recently sent an unsolicited and uncredited article to the Newsletter about the activities of Canadian women in mathematics.

AWM business meeting, San Diego, January 1997. Left to right: Rebecca Struik, Chandler Davis, Lee Lorch (with microphone), Helen Moore, M. Beth Ruskai, Jean Taylor (AWM president 1999-2001).

AWM honored Lee Lorch with a citation in January 1992: “To Lee Lorch, a founding member of AWM.…Lee has often been a thorn in the side of the mathematical establishment. But then, to its credit, so has AWM.” The citation continued, “ [Lorch] pushed tirelessly on issues of special concern to women and minority mathematicians…that mathematics has become more receptive to women and minorities owes much to Lee” [MA92, p.5]. Many other awards have been bestowed upon Lorch, such as an honorary Doctorate of Humane Letters from the City College, City University of New York for, “your distinguished contributions in the field of mathematics and for your lifelong dedication to human rights, justice and equality,…[for your] major contributions to the fields of Fourier analysis and real analysis,…[and for your] equally profound impact on the lives of minority and women mathematicians who have benefited from your efforts to expand opportunities within the American mathematical community” [ND 90].

Male Mentors. The late Lipman Bers and Wilhelm Magnus were both eulogized in Newsletters of the 1990s for their remarkable mentoring and success with women graduate students. Of Bers’ 48 Ph.D. students, 16 were women. Magnus had 14 women Ph.D. students among his total of 62. Harold Widom was also mentioned for his mentoring in the Newsletter; as of 1993, four of his seven students had been women.

What made these men so effective with women students? Here are some opinions of their students and other observers, taken from the 1990s Newsletters, which describe the mentoring abilities and philosophies of these three farsighted men.

In justification of his support of women at a time when a common view was that women were not capable of doing mathematics, Lipman Bers said (in the book Mathematical People), “It never occurred to me that women can be intellectually inferior to men.” His sixteen women Ph.D. students (of 48 total) were Elizabeth Ferentz, Dorothy Levy, Tilla Weinstein, Esther Phillips, Sondra Jaffe, Jacqueline Lewis, Linda Keen, Lesley Sibner, Vicki Chuckrow, Michele Linch, Jane Gilman, Judy Wason, Rubi Rodriguez, Noemi Halpern, Gita Resnicoff, and Hannah Sandler [MJ94]. When he died in 1993, Sadosky observed, “He was a staunch supporter of human rights. He was well known for his contributions to mathematics and to mathematicians, but we especially recognize his extraordinary production of women mathematicians.…We will miss a dear friend. And we will continue to hope for more teachers like him” [JF94].

Keen wrote, “Bers was particularly special as a mentor and teacher. He loved having students and particularly enjoyed having women students.…Bers made [NYU] much more [friendly for women].…Bers will be remembered, not only for the grace of his mathematical ideas but for the man he was. He had an uncanny ability to bring out the best in his students; he knew when to support, when to cajole and when to browbeat.…He was a man of great integrity in his dealings with people.…He was warm, funny and almost always on the mark in sizing up a situation. his passing is a great loss” [MJ94, p.5].

The fourteen women Ph.D. students of Wilhelm Magnus included Joan Birman. She described Magnus’ welcome when they began working, “I was to regard him as ‘family’ and his office as ‘home’—by which he meant a place for experimentation, for trying out new ideas, where one could feel free to make mistakes without shame.” Benjamin Fine says, “Why Magnus had so many women students and students in general, was a function of [his] unselfishness and basic humanity. He was willing to work with anyone who wanted to work in the field and was not intimidating about it.…[This] coupled with tremendous mathematical insight was what led students to come to him. In the department at Courant, where most of the professors were accessible, Magnus was the most accessible.” Harry Hochstadt adds, “What made Wilhelm such a fine teacher was his deep concern for students and his great courtesy. He performed extremely well in the classroom, and that in itself drew students to him. He would never put a student down or hint that anyone was deficient in any way.…[He] was always available.…These qualities helped to attract many students. Women who started graduate work in mathematics had probably encountered more obstacles in their earlier studies than men and therefore appreciated these qualities even more than men.” According to Donald Solitar and Abe Karrass, “As far as the relatively large number of women who worked with Wilhelm, we think it was in part due to Magnus’ nonthreatening manner and his generosity in aiding students’ and colleagues’ research…Wilhelm also had a strong sense of family, and there was a ‘group theory family’.…We treasure many memories of Wilhelm, which reveal his kindness and genuine concern for people, especially people with difficulties” [JA91].

Harold Widom’s Ph.D. student Estelle Basor wrote, “I believe we [Widom’s Ph.D. students] understood not only the strength of his mathematical ability but that his sense of integrity and fairness would never let us down.…We all know that in fact teaching is often neglected in favor of research. I was fortunate to have a teacher and colleague who excelled at both and who inspired many students, especially women, to pursue mathematics.” [JF93].

More men should be added to this list. For example, William Heinzer, Melvin Hochster, Craig Huneke, and Michael Reed have each had many women Ph.D. students and have effectively mentored postdoctoral women. AWM members are invited to send descriptions of helpful male mentors for the AWM Newsletter and the AWM web site.

Articles by Men in the Newsletter. When an article appeared in Science about genetics affecting mathematical ability in women (see Nature vs. Nurture), many men voiced their disagreement. In particular, Ralph Boas described women’s abilities and purported differences in reasoning thus, “For roughly 50 years I have been teaching college mathematics. I have yet to see any difference in the mathematical ability of men and women, except that, on the whole, the women are more capable. This slight difference I attribute to Society’s constant pressure to keep women out of mathematics unless they are very determined” [MJ86]. Also Ernest C. Schlesinger wrote in a letter to his local newspaper, “Since joining the mathematics department of Connecticut [College] 24 years ago, I have always worked with most able and distinguished women colleagues in my field. Moreover, women have been among the very best mathematics students (both before and after the college became co-educational in 1969).…Women are ill-served when told by teachers, parents, peers and now even by the press, that mathematical activity is not suitable for them, or—and this is worse—that they are somehow biologically unfit for this undertaking, for nothing could be further from the truth” [ND86].

Danny Hershkowitz (Technion–Israel Institute of Technology) wrote about the Olga Taussky–John Todd lecture program. Hershkowitz said of Taussky, “She is the ‘grande dame’ of matrix theory and many, myself included, can trace their abiding interest in this area to her infectious enthusiasm for the subject!” [JF94, p. 15]. He also described the recipient of the lecture-prize, Helene Shapiro (Swarthmore), “I have known Helene for 14 years and have had the privilege of working with her and learning from her. I have been especially impressed by the depth of her knowledge of the literature and her ability to trace results back to their source.…Her devotion to her students and to the process and the content of mathematics education exemplifies the very best of the liberal arts tradition.”

Other articles by men in the Newsletter include an exposition by Barry Mazur on Fermat’s Last Theorem [SO93] and Ron Lancaster’s description of his success teaching calculus to high school girls with a graphic calculator and how this experience changed their attitudes towards technology [MA95]. Steven Givant wrote about the successful Summer Math Institute at Mills, organized by himself and Leon Henkin [MJ95, p.14]. This is an intensive six-week program for talented undergraduate women math majors selected nationwide. It is intended, “to help them reach the top of the mathematical ladder, to help them obtain advanced degrees in the mathematical sciences.” James Humphries wrote more on the two-body problem, “Many of the women who got Ph.D.s when I did…married mathematicians who ended up in good research departments, while the women usually found jobs (if at all) in smaller teaching-oriented departments nearby. No one will ever know whether some of these women might, under better circumstances, have developed first-rate careers” [MJ94, p.7]

In addition, male candidates for AMS positions have often made enlightened statements in the Newsletter regarding the underrepresentation of women in our profession. At first such statements were rare; later they became nearly universal.

A panel including Mel Rothenberg, a younger (unemployed) man, and three women on “Are Women Getting All the Jobs?” in January 1994 provided a good model for men and women to work together for the good of the profession on these problems. It was encouraging to see that many men there were interested in promoting and encouraging women, even in light of a backlash for affirmative action [MA94, p.3].

Men’s Concrete Support. Arthur Jaffe, president of the American Mathematical Society (AMS); John Ewing, AMS Executive Director; Gerald Alexanderson, president of the Mathematical Association of America (MAA); Don von Osdol, MAA Associate Secretary; and John Guckenheimer, president of the Society of Industrial and Applied Mathematics (SIAM); have all worked to include AWM in their meetings and activities, in particular helping us to arrange lobbying, workshops, speakers, etc. At the SIAM/AWM workshops, male SIAM officers and members show their support and encourage the new mathematicians by attending their presentations and offering advice.

Several men at granting agencies have been particularly helpful to AWM, such as Lloyd Douglas at NSF; John Pettit and Jim Schatz at the National Security Agency (NSA); Andre von Tillborg at the Office of Naval Research (ONR); and Fred Howes, director of Mathematical Sciences Division at the Dept. of Energy. The directors at the Math Sciences Research Institute (MSRI), first William Thurston, now David Eisenbud, have been receptive and helpful with the Julia Robinson Celebration workshop in 1996 and the planned Olga Taussky-Todd Celebration in 1999. (John Todd has also helped in the planning of the Olga Celebration.) At Exxon, which has been a longtime supporter of AWM projects, Mike Dooley was the first AWM liason person [JA92]; more recently,Robert Witte has authorized our funding from Exxon. Neal Lane, the recently appointed Presidential Science Advisor and former director of the National Science Foundation, met with Sadosky and “expressed interest in learning more about (AWM’s) concerns” about problems for women in mathematics [MA94, p.4].

AWM’s office has been at the University of Maryland since 1993. At the opening ceremony for the new office, University President Brit Kirwan, Dean Richard Herman, and former Mathematics Department chair Ray Johnson (all mathematicians) made welcoming remarks [MA93, p.4]. Many of the men in the Maryland department are long-time members and contributors to AWM; they are proud of their many outstanding women graduate students and the outstanding young women on their faculty, and they have encouraged these women to apply for AWM programs—five of the twenty-one women at the 1997 SIAM workshop were from Maryland. Jim Lewis, chair of the Mathematics and Statistics Department at Nebraska, has given travel funds, release time, and advice to Wiegand while she has served as president. (Lewis recently received an award from the Nebraska Chancellor’s commission on women for his support of women at the university.)

The men on the organizing committee of the 1998 International Congress of Mathematicians (ICM) at Berlin and the International Mathematical Union (IMU) helped with the activities to highlight women (an Emmy Noether lecture by Cathleen Morawetz, a panel, and a lunch), by assisting in finding support and local contacts for the activities and helping us coordinate with the European women and other groups of women in mathematics. In particular, David Mumford of the IMU and Martin Groetschel for the ICM sent many email messages.

Many men have contributed financially to AWM. For example, Dick Schafer was mentioned as making an extra contribution to the Alice Schafer Prize fund [JA92].

Men often nominate outstanding women students for the Schafer prize, and often they have assisted and encouraged these young women. Departments frequently sponsor the prizewinners’ trips to the meeting. They are extremely pleased about the honor the prize brought to their institutions and to the winners they have nominated.

Finally, husbands of women active in AWM have often provided valuable support and assistance to their wives and the organization; particularly we mention Gerry MacDonald (Anne Leggett’s husband) and Jack Quinn (Bettye Anne Case’s husband). While husbands may have an extra incentive to help, they have gone beyond their duty, just as many of the other men have gone beyond what help for women in mathematics normally might be expected of men. Thanks in great part to their support, AWM and women in mathematics have prospered.

Footnotes.

1. Natalie Zemon Davis, a distinguished historian who has been president of the American Historical Association. Their three children were raised while she was at Princeton, he at Toronto.

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