In the Footsteps of Myriad Women MathematiciansSeptember 26, 2005
At the prize lunch in New Orleans, Barbara Keyfitz, president of the Association for Women in Mathematics, read the citation for Ingrid Daubechies, who had given the AWM–SIAM Sonia Kovalevsky Lecture earlier in the week (and who, like Keyfitz, is among the women whose names and stories appear in the book reviewed here by Rachel Kuske). Daubechies, whose talk was titled “Superfast and (Super)sparse Algorithms,” was cited for “fundamental contributions in the field of applied and computational harmonic analysis over the last 25 years” and for the “significant impact” she has had in “numerous areas of applied mathematics and signal and image processing, with research accomplishments bridging many scientific and engineering disciplines.” Daubechies’ “service record is also impressive,” the citation concludes. “She is an inspiration to the entire mathematics community, especially the women's mathematics community.”
Complexities: Women in Mathematics. Bettye Anne Case and Anne M. Leggett, editors, Princeton University Press, Princeton, New Jersey, 2005, 456 pages, $35.
What was it like for the women in the past who pursued mathematical careers? What are the similarities in the situations of women mathematicians then and now? What has changed along the way, and what hasn't?
Case and Leggett have collected talks, biographies, and histories that give us a snapshot of these issues as we view them at the start of the 21st century. Much of the historical material is adapted from workshops, panels, and newsletter articles of the Association for Women in Mathematics, and some is drawn from talks given at international math meetings. Quantitative data is blended in to complement these selections, and a few articles give results of statistical studies or surveys. A number of present-day mathematicians give viewpoints to compare and contrast with the historical perspective. The style of the book is very welcoming; the articles are engaging and should appeal to a variety of readers.
When the articles are read in order, the focus changes as follows. First, we en-counter a number of prominent women mathematicians who lived during the 20th century: Olga Taussky-Todd, Julia Robinson, and Emmy Noether, among others.
Then we step back further in time, considering women mathematicians from the 19th century, including Sonia Kovalesky, Sophie Germain, and Mary Fairfax Somerville. The reader cannot help but be impressed by what these women accomplished in environments that were, to say the least, difficult. From the details of their experiences, some similarities emerge, such as by studying under blankets in cold rooms or by dim nightlamps to thwart their families' attempts to deter them. Some of the individual accounts are linked, either by family connections or by student–supervisor relationships among the women whose stories are told.
The articles in Section II chronicle changes in the mathematical culture that directly impact the involvement and visibility of women, from both individual and group viewpoints. Such developments as the beginnings of the AWM, changes in the American Mathematical Society, and increasing numbers of invitations to women to give prestigious talks through the 1970s and 80s are documented from different perspectives. Inter-national viewpoints are also highlighted; "Voices from Six Continents" is a collection of perspectives from women mathematicians from all over the world.
Section III concentrates on issues that are part of academic careers, pathways in non-academic careers, and the balance of a mathematical career and personal life. These topics are presented mainly through the experiences of individual women mathematicians, with some complementary survey and statistical data. One of the most striking collections of articles in this section covers the double discrimination encountered by African American women pursuing mathematical careers. A large number of women mathematicians discuss issues of geography, lifestyles, choice of career direction, and balance of career and family.
Sections IV and V deal with recent history. The Olga Taussky-Todd Celebration of Careers in Mathematics for Women, held in Berkeley in 1999, is the basis for the material in Section IV. This meeting brought together mathematicians of different backgrounds, and included both technical talks on Taussky-Todd's work and talks on connections to applications. Different career perspectives in industry, academia, and education are included, along with highlights of the conference talks and panels. Section V covers the present day from a variety of perspectives, with personal contributions from both senior and junior researchers at major research universities, national labs, and liberal arts colleges and institutes.
Instead of reading the book straight through, I found myself skipping around a lot. The table of contents made me curious about different topics simultaneously, and I enjoyed the contrasts in reading about different aspects in parallel: academic vs. non-academic careers, the present day vs. the 19th century, and the history of women-in-math organizations vs. activities of such organizations today. Because all the articles are short and self-contained, it is easy for each reader to chart a personal path through the book.
The majority of the articles by and about individuals cover historical or career perspectives. Some of the articles spend significant time on mathematical results, with different emphases. There are summaries of mathematics from earlier days, such as the work of Germain and Taussky-Todd, and technical discussions of different directions in research fields, as well as some specific results, ranging from a nexus of analysis, algebra, and topology to computational methods to statistics to the science of paint.
Another theme that naturally arises, even though it is not necessarily intended as a focus, is the influence of social forces on the careers of these mathematicians: In the 19th century, political and social trends in Russia obliged women interested in studying mathematics to go to western Europe. War and post-war periods influenced job tracks and transitions, also causing ups and downs in hiring trends for women. Equality movements in the 70s led to changes in mathematical societies and to the founding of the AWM.
In its mix of articles, the book gives an overview of the changing complexities en-countered by anyone who pursues a mathematical career. As a result, a reader can come away with a variety of messages. As proposed in the dustjacket copy and preface, the book certainly provides inspiration for those just starting their careers, and women in the field today may find elements of their own experiences in the biographies of the women portrayed in the book.
Some of the book's subjects made their way by traversing many different areas, both mathematically and geographically, while others found more direct paths in their careers. But a common message that comes through is the talent and dedication that stood them in good stead even when circumstances seemed to conspire again them.
The complexities discussed in the later chapters are not limited to women mathematicians, even though, as shown by some of the statistics presented, a number of the issues are more likely to play a role in the careers of women. The book captures a wide range of experiences, and many of the biographies or personal vignettes could be interesting or inspiring for any person in the field, young or old, of either gender. For mathematicians and scientists at all levels, these articles contribute to recent efforts to better understand how diversity issues have changed over time, what improvements have been made, and what challenges are often encountered today.
The picture of the elements in the field impacting women today is no less compelling for being compiled mainly from anecdotal evidence rather than hard data.
Given the sometimes disturbing history of the treatment of women in science careers, one might imagine a reader finishing the book with a taste of frustration or negativity. On the contrary, the overall the tone is positive, and this serves the purpose well. While the book does not give an entirely rosy picture of the representation of women at all stages of mathematical careers, it certainly makes it clear that the climate has improved. As to the question of how the numbers of women can be increased, no answer is given, but that is not the purpose of the book.
Tracing the changes over time, the articles illustrate that some of the obstacles to diversity in the field today may be more subtle and, as the title suggests, more complex. This snapshot contributes to present-day efforts toward awareness of the tangles that still exist. Perhaps another snapshot down the road will show if we have worked out some of the knots.
Rachel Kuske is an associate professor of mathematics at the University of British Columbia.