Report on the Berlin ICM
Sylvia Wiegand

Reprinted from AWM Newsletter, 28(6), November-December 1998, pp. 3-8.

The International Congress of Mathematicians (ICM) held Aug 18-23 in Berlin included many wonderful activities, and all went smoothly due to the impressive organization of the event. Organizer Martin Groetschel said, "We're not professionals like the AMS, so we work harder." Martin took great care with each small detail of the part of the program highlighting women in mathematics.

The events highlighting women, cooperatively organized by the AWM, the European Women in Mathematics (EWM) and other groups of women in mathematics, were marvelous. They included a panel discussion featuring women with varied perspectives from many different countries, a film on women in mathematics in several countries, a special Emmy Noether lecture given by Cathleen Morawetz, and a congenial lunch gathering of about fifty people. (Web editor's note: Check out the pictures from ICM '98 too!)

The ICM98 Opening Ceremony was a gala event featured on German national TV (and re-run for several days afternwards). Chamber music was interspersed with general mathematics talks such as "Trends in the Profession of Mathematics" by David Mumford, and "Reflections on the Future of Mathematics" by Avner Friedman.

In conjunction with the Congress, there were various mathematics-related exhibits: Springer memorabilia and history, "Mathematics and Ceramics", and "Terror and Exile" (which documented the persecution and expulsion of Jewish mathematicians from Berlin between 1933 and 1945). A special ICM stamp was issued in commemoration of the Congress, and we had the opportunity to buy a stamped and dated souvenir of this event.

Andrew Wiles' talk on "Twenty Years of Number Theory" concerned finding rational points on elliptic curves; a captivating inspiring lecture even if you had to watch it in another room on a movie screen---every seat and every space in the aisles of the main auditorium were taken. 1998 AWM Noether Lecturer Dusa McDuff's beautiful plenary lecture at the Congress included marvelous pictures of simplectic folding.

Progress report: How many women speakers?

Always AWM gives a "Progress Report" on the ICM. The number of women speakers there is an indication of how women have advanced in mathematics and how well their achievements are recognized. This time, Dusa was the one woman among twenty-one Plenary Lecturers. But Cathleen's lecture, in a plenary slot, was given to an overflowing crowd who received it enthusiastically. There were eleven other invited addresses by women out of a total of 165. For comparison, before the 1990s, Emmy Noether in 1932 had been the only female Plenary Lecturer at any ICM. Then in 1990 (Kyoto) Karen Uhlenbeck became the second woman Plenary Lecturer; in 1994 (Zurich) there were two, Ingrid Daubechies and Marina Ratner [AWM Newsletter, May-June 1994, p. 2]. In 1994 eight other women delivered Invited Addresses at the ICM out of a total of 152, and AWM and EWM jointly sponsored a Special Emmy Noether Lecture given by Olga Ladyzhenskaya.

The ICM panel on women

Bhama Srinivasan (chair; Chicago, U.S.), Bettye Anne Case (Tallahassee, U.S.), and Christine Bessenrodt (Magdeburg, Germany), were the organizing committee for the panel discussion "Events and policies: Effects on women in mathematics", sponsored by AWM, EWM and the Committee on Women and Mathematics of the European Mathematical Society, formed. The panelists were: Inna Yemelyanova of Novgorod State University in Russia. Minping Qian from China, Dusa McDuff of the U.S., Mary Glazman from Mexico, Ljudmila Bordag of Germany, and Claire Baribaud of Switzerland. Christine Besserodt moderated and Bhama Srinivasan and Bettye Anne Case (representing AWM) also presided. The text of the panelists' remarks and photos will appear in the January-February issue of the newsletter.

There were about 170 people in the audience, about half of whom, surprisingly, were men (or maybe not so surprisingly because most of the attendees of the whole ICM were men). Most men who spoke and the men I recognized in the audience were supportive of women, particularly Bernhard Neumann, who was one of the founding members of AWM and whose late wife Hanna Neumann was also a well-known mathematician

Yemelyanova gave some statistics about faculty in the sciences at her university (ranked fifth in Russia): Among the full professors, there were 90 men and 2 women (2.22%), and among all the instructors with Ph.D.s 311 men and 71 women (22.93%). But of those who were labeled "Chiefs" among the Ph.D. instructors, 84 weremen and only six were women (7.14%). Of those instructors without degrees 72 are men, 65 women. She thought that women do not have an equal chance, and she was especially concerned about the plight of school teachers in mathematics, of which 85-90% are women--she said 67.7% of these teachers are on the brink of poverty. Yemelyanova also told me later that her salary and salaries generally are very low; her trip to the ICM cost her about five months' salary. Yemelyanova mentioned a Russian colleague she wished had come to Berlin to join the discussion; this other woman organized a Russian Association for women in mathematics five years ago. Their Association has held six conferences for Russian women in mathematics.

Qian spoke about an unfortunate change in China in the past 10 -15 years. Previously men and women had an equal chance to study mathematics in the cities, although in the country, that wasn't true. But now it is more difficult for women. She has seen cases where the only reason a woman couldn't get a job was because she was a woman. Employers asked first whether the candidate was a woman, and if so, said "we have too many women."

McDuff's conclusion about the situation in the U.S. was that it "needs work, but isn't bad". She mentioned that the right-wing is trying to defeat gains for women, but said that there are many positive signs, for example sexual harrassment charges have been successful. The U.S. needs to improve achievement and interest in mathematics and science for both boys and girls---The TIMMS study shows that 12th grade mathematics achievement in the U.S. is dismal. At Stoneybrook, there is a WISE (Women in Science and Engineering) group which holds special workshops for women.

Glazman says the economic crisis in Mexico has affected women in mathematics---salaries for professors aren't enough or even half enough. Many have left their jobs. The investments that universities made are being destroyed. In general women are recognized in Mexico to be good administrators; they are often chairs of departments, a woman is president of the Mexican Mathematical Society, and women speakers are more popular and better understood because they try harder to be understood. But in mathematics departments women are rare at the high levels.

Bordag was born and earned her Ph.D. in Russia, but when she married a German physicist he couldn't get a position in Russia, so they moved to Germany. But at Leipzig after they came, the staff was reduced from 10,000 to 2000. Faculty were told they could take a temporary job or leave. She had a temporary position for six years, then many more lost jobs. When the positions were cut, women were more often affected; the present ratio of women to men is much lower than before.

Baribaud, a 1996 Ph.D. is already in her third position (first a postdoc, then at Lausanne, now at Zurich). She says that in Switzerland fifty per cent of the baccalaureate degrees go to women, thirty per cent of the masters degrees and only ten per cent of the Ph.D.'s. Most women mathematicians do applied mathematics because it is easier to get jobs. Often women get jobs at banks. There aren't many academic jobs in Switzerland. In the academic system there, new Ph.D.s are 25 to 35 years old, and people aren't promoted to Professor until at least age 40. And the salaries are very low before that. Women usually stop before that is possible. She is also familiar with the situation in France; it is better there, not because of any affirmative action but because there are more positions.

Members of the audience made interesting comments. (Unfortunately their names weren't always easy to hear.) Neumann remarked that in the whole history of the Royal Society of London, there have been only two women members: Mary Cartwright who recently died at age 97 and Dusa McDuff. Before the 1930s there were at least 12 creative women active in the AMS, including Anna Pell Wheeler. After that there was a big gap in the participation of women. Now again they are active. Why is that?

Srinivasan asked about childcare in the various countries; the panelists mainly said that it's not a problem for them and that husbands do some of the childcare and housework. Bordag mentioned that after the unification of Germany, less daycare is provided than in the former East Germany. (That was one of the good parts of communism.) A man in the audience asked: "How can women be mathematicians and also take care of their children and kitchens?" Also in the audience, Cathleen Morawetz answered, "It's quite easy; I have four children and six grandchildren, and I have devoted a lot of time to them. It's possible to do this and have a nice career." She later admitted that it might not be so easy, but it was an effective response!

A woman from Barcelona pointed out that we need to change the values of our societies. Something is wrong if we are fixed in outdated historical traditions and customs, such as for childcare. Lots of women and men have children. It's not a question of how women fit int this society but of making another kind of society. It is worth the effort to do so.

A man from India, a mathematician, whose late wife was a teacher and whose three children and their children are teachers, said it is disturbing that the position of women is not good in all countries. In the global social order, women work on average two-thirds of their days, men only one-third. But women get 25 per cent less pay. In the U.S. there has been no woman president or even vice-president.

EWM Film

After the panel discussion we viewed a fascinating film produced by the EWM, giving a profile of four women mathematicians. from France, Germany, Britain and Spain. It was interesting to see how varied their situations were in the different countries. One speaker mentioned that in countries where permanent positions are given later in life, it is harder for women to advance in mathematics. The women in Germany and England had more problems, and the women from France and Spain had fewer, with the situation described for Spain sounding the most inclusive of women.

Cathleen Morawetz' lecture

Morawetz, introduced by her former student Irene Gamba of Texas, began by saying "In my heart I know this honor for women would have been impossible forty years ago. And I hope that thirty years from now it won't be necessary." She spoke briefly about Emmy Noether, "the queen of the mathematical sciences", who was a non-religious Jewish refugee from Nazi Germany and died at age 54---she didn't live "to receive the accolades she deserved, nor to know of the terrors of Jews, of Stalin, nor of the appalling destruction of Europe."

Morawetz talked about conservation laws for the time dependent wave equation obtainable from some work Noether had done. Noether had not liked it much---"it was too messy!"---but it has generated many applications. Then Morawetz switched gears and discussed black holes, describing how they are created by the death of a star and giving related equations. The following paragraphs are from the program brochure.

Emmy Noether Lecture: Born 1882 in Erlangen, Bavaria, Germany, Emmy Noether persisted in the face of multiple obstacles to become a renowned algebraist. At Go"ttingen 1915-1933 she taught (Hilbert sometimes had to list her courses under his name), wrote on a remarkable range of topics (e.g. general relativity), edited and contributed to the published work of others. Before her untimely 1935 death at Bryn Mawr, Pennsylvania, United States, she had directed many students and collaborated with colleagues on both sides of the Atlantic. For more information on Noether see also: http://www-history.mcs.st-andrews.ac.uk/history/Mathematicians/Noether_Emmy.html

Abstract of lecture: The time dependent wave equation has many conservation laws obtainable by using Emmy Noether's theorem for equations coming from Lagrangians. From this nucleus we survey some estimates that can be found for equations close and not so close to the wave equation and show what these estimates are good for (time decay for exterior problems and nonlinear Klein-Gordon, for the reduced wave equation and for the Tricomi equation). On a slightly different note, some weakly quasi and other nonlinear perturbations of the time wave equation have simple formal asymptotic solutions. These formal solutions probably represent real solutions but that requires some new estimates.

Cathleen Synge Morawetz: Born in Toronto of Irish parents, she graduated from the University of Toronto in 1945 and went on to receive her master's degree at the Massachusetts Institute of Technology. She earned her Ph.D. at New York University, with a thesis on the stability of a spherical implosion. She is Professor Emerita at the Courant Institute of Mathematical Sciences at NYU, where she served as director from 1984 to 1988. In 1981, she delivered the Gibbs Lecture of the American Mathematical Society and in 1982 presented an Invited Address at a meeting of the Society for Industrial and Applied Mathematics. In 1983, she presented the AWM annual Noether Lecture at the (U.S.) Joint Mathematics Meetings. She is a member of the National Academy of Sciences and was named Outstanding Woman Scientist for 1993 by the Association for Women in Science. She was the second woman president of the AMS, serving from 1995 to 1997.

Morawetz's earliest published works ere on the stability of steady viscous flows. In the fifties, she turned to the mathematics of transonic flow and showed that specially designed shockless airfoils develop shocks if they are altered even by a small amount. The discovery opened the problem of developing a theory for transonic flow with shocks. Much of her research has focused on the wave equation. The classical problem of whether light should be treated as waves or as streams of particles can be answered, "either will do," if it can be shown that high frequency waves are, asymptotically, streams of weightless particles moving along rays. With D. Ludwig, Morawetz showed that this is true for a medium with constant light speed outside a relecting star-shaped object. She used related methods with Walter Strauss to study the behavior of a semilinear wave equation. Throughout her career, Morawetz has turned to developments in computations working with A. Bayliss, G. Kriegsman, and T. Wolfe. In her Noether Lecture, she showed a film generated by computer of some unexpected nonlinear laser effects. Today, her interests are divided between working in fluid dynmaics, mainly the mathematics of transonic flow, and on the propagation of waves.

Morawetz's father was the mathematician J.L. Synge, and her mother also studied mathematics for a time. Both her parents were supportive of her interest in mathematics and science, and it was a woman mathematician, Cecilia Krieger, who had been a family friend for many years who later encouraged Morawetz to pursue a Ph.D. in mathematics. A mother of four, Morawetz has been able to balance her energies between her research and her family. She was honored by the National Organization for Women for successfully combining career and family; today her main nonmathematical interests are her six grandchildren---and even there she likes to do things which keep them interested in science and mathematics.

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