Michèle Audin has my number: “Although mathematicians hardly know Sofya Kovalevskaya’s work, they have all seen her portrait.” I have even participated in Sonia Kovalevsky Days,* events to help get girls interested in studying math. I knew Kovalevskaya was a groundbreaking woman mathematician but knew almost nothing about the details of her life and work.
When I stumbled on Audin’s book Remembering Sofya Kovalevskaya (published in French in 2008 and English in 2011), I decided it was time to rectify the situation. It ends up that this book is no ordinary biography of a mathematician. As Audin writes in the introduction, the book is not a history book. It’s also not a math book or a novel. It’s an eclectic and idiosyncratic work that defies an easy label. Set your expectations aside when you read it. In the wise words of Marcel the Shell, “Really, what you just have to want to do is take a ride.”
Kovalevskaya was born in 1850 in Moscow. She entered a marriage of convenience in 1868 so she could leave Russia, eventually ending up studying under Karl Weierstrass in Berlin. The university did not allow female students, so he taught her privately, and she got her doctorate from Göttingen in absentia in 1874. After receiving her degree, she was unable to get a job for a few years and gave birth to her daughter. Eventually she got a job in Stockholm as a Privatdozent (an academic rank below professor that allows someone to teach) thanks to the efforts of Gösta Mittag-Leffler. In 1888 she won a prestigious prize, which made it possible for her to get a permanent position as a professor in Stockholm. Unfortunately she died shortly thereafter. She was a polyglot, fluent in Russian, Polish, French, German, English, and Swedish. In addition to her mathematical career, she wrote novels and plays.
I was struck by how modern Kovalevskaya’s career sounds today. Audin writes, “She is without doubt the first woman to have had a professional university career in the way we understand it today: she proves original theorems that earn her the title of doctor, she gives courses, she concerns herself with politics, she believes in the responsibilities of scientists, she travels, she proves more theorems, she participates (without much enthusiasm) in committee meetings, she has a daughter, she is editor of an international journal (Acta Mathematica), she fights for women’s rights, she attends and contributes to scientific meetings, she’s up for promotion, she writes reports and letters of recommendation, she travels to meet with colleagues at other universities.” Far from being a pariah because she was a woman, she was a respected member of the mathematical community.
Kovalevskaya worked on several problems in the broad area of analysis. Her doctoral thesis consisted of three papers on three different topics, any one of which would have been sufficient to earn a degree on its own. They covered partial differential equations, abelian functions, and the shape of Saturn’s rings. Her most important work later in life was on the movement of a spinning (that is, moving with one point remaining fixed) solid like a top. Euler and Lagrange had solved the two simplest types of tops, and Kovalevskaya found another type of top that could be analyzed. It was this work that earned her the Bordin prize in 1888. Audin encountered Kovelevskaya through the Kovalevskaya top and goes into the most mathematical detail in the chapters dealing with Kovalevskaya’s work on that problem.
In spite of her success, though, Kovalevskaya did face obstacles, and her reputation has gone through ups and downs. Some damage was due to the discovery, posthumously, that one of her papers had a fatal error, an unfortunate situation that does happen every once in a while to even accomplished, careful researchers. And some was due to people's prejudices about the proper role and behavior of women.
While reading this book, I happened to reread Francis Su’s Mathematics for Human Flourishing, the address he gave as the retiring Mathematical Association of America president in January. In it, he ruminates on this quote from philosopher Simone Weil (sister of mathematician André): “Every being cries out silently to be read differently.”
Audin’s book is as much about Kovalevskaya’s relationships with mathematicians past and present as it is about her own life and work. As Audin listed some of the indignities she faced and her reputation still faces — the “white” marriage she entered in order to have the freedom to leave Russia so she could study math, her salary woes, the ongoing questions about whether she was really independent from her advisor Karl Weierstrass, the endless comments about her appearance — I was crying out silently for Kovalevskaya to be read differently. For her not to be a canvas for other people’s projections of what women and mathematicians should be. That feeling was most poignant in chapter 11, “I remember Sofya, by George, Gösta, Julia and all the rest.” In it, Audin collects excepts of letters or other writing about Kovalevskaya people who knew Kovalevskaya during her life and those who knew her by reputation and rumor after her death.
For example, Audin includes this excerpt from a letter by Carl Runge, another student of Weierstrass:
On Saturday we had a very interesting party at her flat. The company consisted of Mrs. Kovalevskaya and four young mathematicians, and we talked as we usually do. She is about 30 years old, her face is delicate, thoughtful, a little sad [this was two months after Vladimir’s suicide], and quite charming when she smiles. It was strange for me to talk of mathematics with a lady and to be able to discourse with complete freedom. She knows the subject well. I knew this especially when she asked me about my work by the excellent questions she put. Before, I had imagined her to be sharp-nosed, old-looking, and with spectacles, but I was amazed to find that a scientific education can match such a perfect feminity[sic].
As Audin wryly observes, Runge’s surprise that Kovalevskaya could be a good mathematician and an attractive woman shows that “the stereotype can exist before the species.” Reading recollection after recollection, I felt Kovalevskaya being buried under layers of other people’s perceptions and beliefs.
Like Sophie Germain and Emmy Noether, two other early women in math, Kovalevskaya died young. She was only 41 when she contracted pneumonia while traveling between Genoa and Stockholm. Telling that story, Audin writes,
Again, it’s winter, it’s Denmark, it’s cold, it rains or it snows, there’s wind on the railway platforms, on the ferries, on the way from one to the other. And then, surely, Sofya is sick when she arrives in Stockholm. Apparently not too much at first because she teaches her class, the first class of the semester, February 6, a Friday, she then goes to a gathering at the Gyldéns in the Observatory, which she leaves early because she feels feverish, she takes the wrong omnibus, it is cold ... She gets worse and she takes to her bed. On Monday she seems better, she speaks with Mittag-Leffler about her ideas on Euler’s equations.… But her illness has turned into pneumonia, it’s the 19th century, forty years before the discovery of penicillin ... you die of pneumonia, even if you are a brilliant scientist of forty-one, even if you have lots of scientific, personal and literary plans, as did Sofya, as she said, as she wrote to her friends before becoming sick, you die even if you are happy, as Sofya was at that time, and then, that’s what Sofya does, she dies of it.
Audin’s distinctive voice makes Remembering Sofya Kovalevskaya a fascinating and moving book. It is not a substitute for a traditional biography, but it is a compelling read for anyone interested in seeing Kovalevskaya in a different light.
*Audin prefers the spelling Sofya Kovalevskaya, but many transliterations of Kovalevskaya’s name exist, as Audin points out in the book. In most of this review I’m following Audin’s lead and using Sofya Kovalevskaya.