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 homeby 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 Widoms Ph.D. student Estelle Basor wrote, I believe we [Widoms 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 womens 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 Societys 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, orand this is worsethat they are somehow biologically unfit for this undertaking, for nothing could be further from the truth [ND86].
Danny Hershkowitz (TechnionIsrael Institute of Technology) wrote about the Olga TausskyJohn 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 Fermats Last Theorem [SO93] and Ron Lancasters 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.Men and AWM Panels. Wise, witty and caring men have added sparkle and enlightenment to many AWM panel discussions over the years. For example, Richard Tapia led a discussion of pipeline issues (how to get more women in mathematics) and introduced graduate students from Rice (including many women) at a panel at the International Conference on Industrial and Applied Mathematics Workshop in the summer of 1991 in Washington, D.C. Robert Williams, spouse of mathematician Karen Uhlenbock, spoke in the January 1993 panel in San Antonio, Is Geography Destiny? on the effect of the two body problem. Craig Huneke and Steve Kennedy, panelists on Mathematicians and Families at Baltimore in January 1998, described their cooperative arrangements with their spouses and the joys of fatherhood [MA98]. At the 1997 SIAM workshop, Lloyd (Nick) Trefethen gave an outstanding talk on writing mathematics [ND97]. Several men have served on more than one AWM panel, such as Hugo Rossi and Jagdesh Chandra.
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].
Mens 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 (AWMs) concerns about problems for women in mathematics [MA94, p.4].
AWMs 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 programsfive 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 Chancellors 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 Leggetts husband) and Jack Quinn (Bettye Anne Cases 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.