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Remembering Sofya Kovalevskaya

Michèle Audin
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[Reviewed by
Michael Caulfield
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A key to understanding Michèle Audin’s Remembering Sofya Kovalevskaya (Springer, 2011) is found in the word “remembering.” This book is not a biography, nor is it an exposition of Kovalevskaya’s mathematical accomplishments, although it definitely includes elements of both. It is rather a collection of thoughts and observations on the personal and professional life of a mathematician that Audin clearly feels does not receive her due.

It is in the final chapter of the book that we discover the author’s history with Kovalevskaya. Audin began to encounter her mathematical work in the 1990s and, over a 10 to 15 year period, became more and more fascinated by the details of her life and work. Audin became a consultant for a play written on Kovalevskaya’s life and did radio interviews about her in France. She makes clear throughout the book that a significant motivation for her work in writing this book is to counteract the negativity that women mathematicians in general, and Kovalevskaya in particular, have to suffer.

The early chapters of the book provide a listing of the events in the life of Sofya Kovalevskaya (1850–1891), written in two-column format so that they can be compared to contemporary world events of the period. They also include a collection of stories illustrating certain events in Sofya’s (as Audin most commonly refers to her) life. Most of the stories are personal, rather than professional, in nature. Here we also read an exposition of the many forms “Sofya Kovalevskaya” has taken when translated from Russian to English and why Audin has chosen this version. (Audin, of course, is French.)

In Chapters IV and V we come to a discussion of Sofya’s most significant mathematical contributions, the Cauchy-Kovalevskaya Theorem and her work on the motion of a solid. Audin includes many references, including both contemporary and later reactions to the work as well as related results from the 20th and 21st centuries.

Proceeding through the book we learn of Sofya’s relationships with Mittag-Leffler, Weierstrass, and others, and how they helped her to eventually secure a position at Stockholm University, a rarity for a woman at the time. We see her selected to the editorial board of Acta Mathematica. We also learn that during these years she frequented the company of revolutionary socialists and described herself as a “near nihilist.”

There is a long discussion in Chapter IX of Sofya’s reception of the Bordin Prize and the ensuing controversies, then and now. How much of her work was original? Was she only developing Weierstrass’s ideas? Audin takes the opportunity here, as throughout the book, to defend Kovalevskaya and all women mathematicians. She asks why these kinds of objections are raised more commonly about female mathematicians than male ones. And she points out that Weierstrass had many prominent students but that Kovalevskaya is the only one whose reputation is dogged by these “not original” suspicions.

The book concludes, just before the author’s recounting of her own personal history, with a long series of usually short quotes from people who knew Sofya or who were commenting later on her life and work. These quotes are arranged chronologically. Most of the remembrances are fond, but some objected to her position in Stockholm, or even wondered whether a woman could ever be properly called a mathematician at all. Of course, it is these very comments that Audin is striving to overcome throughout the book.

Audin’s writing style is not typical. Her book includes wide margins, which are filled more often than not with comments elucidating the topic of the text on the page, or giving more background on an individual or mathematical topic being discussed, or perhaps simply including the author’s’ musings or opinions. She also includes interludes of what might be called historical fiction in which she paints a detailed scene, including dialog, of a particular period in Sofya’s life.

Most jarring is the widespread lack of chronological continuity found throughout. This is a book of remembrances and Audin feels no constraint to tell her story in sequence. It is very much like sitting down with her and having the conversation take whatever turn it will. One illustration of this is that a footnote on page 111 refers both to page 46 and to page 130. For those who are not already familiar with the life of Sofya Kovalevskaya, this pattern of writing may induce confusion, as Audin sometimes refers to an incident or a person before that topic has been discussed.

Michèle Audin set out to tell us of a woman and a mathematician, Sofya Kovalevskaya, for whom she clearly feels a great fondness. She wants us to see Sofya as a mathematician who accomplished great work, and as a woman who lived a difficult, yet rewarding life. She tells us that Sofya’s last words were “Too much happiness.” Given the struggles we learn of as we read Audin’s pages, it is a remarkable final thought.

Michael Caulfield is a Professor of Mathematics at Gannon University in Erie, Pennsylvania. His writing is focused on mathematical topics of historical interest. His career in mathematics began when he was a member of an “Outstanding” team in the COMAP Mathematical Contest in Modeling.

See the table of contents in the publisher's webpage.