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Against All Odds Women’s Ways to Mathematical Research Since 1800

Eva Kaufholz-Soldat and Nicola M.R. Oswald, eds.
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The Basic Library List Committee suggests that undergraduate mathematics libraries consider this book for acquisition.

[Reviewed by
Jemma Lorenat
, on
Against all Odds: Women’s Ways to Mathematical Research Since 1800 (Springer, 2020, Cham, editors Eva Kaufholz-Soldat and Nicola M. R. Oswald) grew out of a “small conference on women in mathematics in Würzburg in 2015” followed by a workshop “Women in Mathematics: Historical and Modern Perspectives” at Oberwolfach Research Institute for Mathematics in 2017. Evidence of this sustained, collaborative approach is apparent in the interchapter citations, conversational tone of certain chapters, and the unifying programmatic understanding that “it is simply impossible to craft history without adopting the present as a research objective” (Govoni, 287). The book’s central question – “What did it take for a woman to become a mathematician?” – informs the present and future of women in mathematics. 
Temporally, the book begins with Sophie Germain and concludes with interviews of current practicing Danish women in mathematics. Geographically the scope is European including “mathematicians in Italy, Poland, the Czech Republic, Germany, Denmark, France, and Great Britain’’ among whom several emigrated to the United States as a result of World War II (Kaufholz-Soldat and Oswald, xvii). A chronological introduction serves to link these 200 years of history through “important milestones in the timeline of women’s education” (vii). The book is organized thematically in four parts: institutions, couples, approaches, and perspectives. Along with the global introduction by Eva Kaufholz-Soldat, the first three parts begin with “Introductory Reflections” by Nicola Oswald. 
The parts are defined both by content and methodological approach. “Institutions” considers four different universities and the women who attended them from the late-nineteenth through early-twentieth centuries. These chapters rely on administrative archival research in order to provide thorough local prosopographies. “Couples” also utilizes unpublished sources, but in these biographical treatments personal correspondence and manuscripts are more central. Between these two parts, the focus shifts from education to careers, together illuminating life cycles of women in mathematics. “Approaches” tracks “intended or generated strategies of selected female mathematicians” and asks how “to derive meaningful statements on the basis of biographical material” (Oswald, 182). Finally “perspectives supplements history with more sociological and philosophical treatments. These final two chapters step back to consider the functions of the history of women in mathematics and how they might serve to support the present. Are “biographies of successful – or unsuccessful – women in math and science […] useful tools for attracting girls to and sustaining women in maths and science”? (Govoni, 287) How can prosopography help “in granting a voice to those who have been forgotten by history” (288)? The book thus exemplifies the possible fruitfulness of interdisciplinary collaboration.
The introductions and final section provide a synthesis between texts, but each of the remaining chapters also has the potential to stand alone. For a course in the history of mathematics, these chapters are valuable in drawing attention to diverse ways in which women have entered mathematics and persevered in it. They also serve as frameworks for future research --- demonstrating the potential of each college or university’s local archive and how to structure, execute, and represent interviews with living subjects. In particular, I have already directed students to Jenny Boucard’s “Arithmetic and Memorial Practices by and around Sophie Germain in the 19th Century” as an excellent example of metabiography and Renate Tobies’ “Internationality: Women in Felix Klein’s Courses at the University of Göttingen (1893—1920)” to provide a more robust understanding of the environment where so much contemporary mathematics took root.
That said, in reading the book cover-to-cover reoccurring motifs stand out that might pass off as anecdotal in a more piecemeal selection. 
For instance, there is a persistent and depressing provincialism in the status of women across national boundaries. Much of the book centers on the turn of the twentieth century, an era when mathematicians prided themselves on their international cooperation. Yet the right for women to attend universities had to be hard-won at the level of each nation or institution. Even at the institutional level, the admittance of some women by no means guaranteed such opportunities for all. The situations in Zürich, Göttingen, and Bavaria illustrate how “foreign female academics paved the way for German [and Swiss] women who were willing to study” (46). The slow, sisyphysian efforts for women to attend mathematics lectures, earn doctorates, and finally hold academic positions transcend different political histories. Martina Bečvářová’s description of “women in the Czech lands” is paradigmatic:
In the first half of the nineteenth century, higher education for girls and women was almost unheard of. The reason is that a woman was supposed to be a good wife, mother, and patriot – she should bring up children with care, responsibility, and in the spirit of patriotism, thereby ensuring public respect for her family. If necessary, she should help her husband to run his trade. Public educational institutions for women as well as private ones (mostly religious and aristocratic) were rare and conformed to the above idea of women’s mission. (Bečvářová, 75)
Moreover, those who argued against the participation of women in mathematics framed historical examples of women and institutions as warnings or failures (see Kaufholz-Soldat and Oswald, vii–xiv and Boucard, 205–206). 
From a more historiographical standpoint, the book also underscores the fruitfulness of reassessing earlier biographical and autobiographical accounts of women in mathematics. This is most apparent in the “Approaches” section, but it also shines through in the strategic presentations of women in couples, who “supported the work without official acknowledgement as a co-author” in order to boost their husband’s chances of acclaim (Vogt, 145). The potential for antiquated biography is true across any subject, but particularly so for marginalized populations whose stories bear the mark of popular prejudices at the time of their writing. 
Perhaps the strongest thread through the book is the power of role models. The editors note that the historiography of women in science, at least since the 1980s, has an agglomerative quality – this book is“another tile in the yet incomplete mosaic that is the contemporary history of women in scientific disciplines” (xvii). One aim in disseminating this history is to demonstrate the existence of women in mathematics. However, as Lisbeth Fajstrup, Anne Katrine Gjerløff, and Tinne Hoff Kjeldsen discuss in their concept of the “implicit girl,” to be one of these first women carries a certain pressure (273–275). Paola Govoni explores this idea further, including the “conviction that women or girls must be exceptionally gifted and prepared for heroism in order to dedicate themselves to science or mathematics” (309). One possible solution she proposes is to “bring students into contact with contemporary women who enjoy satisfying careers in both universities and the private sector while maintaining “normal” personal lives” (311). As Felix Klein observed in 1897, “extraordinary cases” of women in mathematics “would not prove very much” as compared to “our average experiences in Göttingen” (Tobies, 27). The burden of the exception is somewhat relieved in recognizing the collective, in which your own mistakes become statistically insignificant.
The book is a pleasant read and should appeal to a wide audience across disciplines. There are no mathematical prerequisites to full comprehension and as an introductory text the meta-discussions contain robust citations to the past century of the historiography of women in science. 
There are a few minor inconsistencies at the level of publication. Some in-text citations correspond to no bibliographic reference, the table of contents omits the author of the epilogue (Andrea Blunck), and not all participants have accompanying biographies. A global index would have also been appreciated as there are common persons and places across the chapters. These complaints are minor. I strongly recommend the adoption of this book for individual or classroom use.
Jemma Lorenat is a historian of mathematics who teaches and researches at Pitzer College in Los Angeles County. She is writing a book about becoming a mathematician at Bryn Mawr College in the Progressive Era.