Sometimes, being first isn’t what it is cracked up to be. This is particularly true if you are the first woman to achieve recognition in what is considered a solely masculine area. Sofia Kovalevskaya (née Korvin-Krukovskaya), was not only a great mathematician, she was the first woman in modern Europe to gain a doctorate in mathematics, the first woman to hold a university chair in modern Europe, the first woman on the editorial staff of a mathematical journal, as well as a writer and advocate of women’s rights. Being first means a constant struggle against the current of tradition and opposition to change.
As a young child Sofia was fascinated with the unusual wallpaper on the wall of her bedroom, the lecture notes on Mikhail Ostrogradsky and his interpretations of differential and integral calculus. Who knew that a money saving measure would be so inspirational? The family’s tutor, Yosef Malevich, took note of her interest, and at age eleven, Sofia undertook her first proper study of mathematics.
Her father wasn’t supportive of her maths studies, at least, not at first. He put a stop to the lessons, but it was too late for Sophia, as mathematics was now her passion. She snuck a copy of Bourdeu’s Algebra into her bedroom and she read it at night when the rest of the household was asleep (I used to sneak books too, but not maths texts).
Professor Tyrtov, a friend of the family and a neighbour, presented her family with a physics textbook which he had written. and Sofia attempted to read it. She did not understand the trigonometric formulae and attempted to explain them herself. Professor Tyrtov realised that in her working with the concept of sine, she had used the same method by which it had been developed historically. This inspired him to argue with Sofia’s father that she should be encouraged to study mathematics further, rather than waste her intelligence and interests. Sadly, it was several years before he was finally agreeable to allow Sofia to take private lessons. I suspect her mother may have had some influence, as she was a scholarly woman in her own right.
The tutor her family hired was A. N. Strannoliubskii, a well-known advocate of higher education for women, who taught her calculus. Strannoliubskii wrote scholarly articles on education, such as ‘The Procedure for Determining the Position of a Teacher Beginning in the City Schools in the City of St Petersburg’ and ‘Insolency’, which was a critique about the city’s educational policies. (Both those article title translations were made by me using Google Translate. I apologise if they are incorrect.) At the same time, Sofia began an exploration of the philosophy of nihilism, with the encouragement of her local priest. One can only wonder at how her intellectual horizons were expanding during this time in her life.
Sofia wanted to go onto study mathematics at university; Russia at that time didn’t allow women into institutions of higher learning, and so she made the decision to go abroad to study. Her father would not allow her to leave home to study at a university, and women in Russia could not live apart from their families without the written permission of their father or husband. So, Sofia hit upon a novel solution. At the age of eighteen, she entered a nominal marriage with Vladimir Kovalevski, a young palaeontologist. It was meant to be a marriage in name only. They emigrated from Russia that very same year.
You might think Sofia’s problems with getting an education were over, but they were just starting. When Sofia tried to enrol in the university at Heidelberg, she discovered women could not matriculate at the university. Eventually, she was able to persuaded the university authorities to allow her to attend lectures unofficially, provided that she obtain the permission of each of her lecturers, among whom were Hermann von Helmholtz, Gustav Kirchhoff, and Robert Bunsen. She certainly impressed Professor Leo Königsberger, mathematician and science historian, because in 1871, she moved to Berlin to study with Professor Königsberger’s teacher, Karl Weierstrass, considered the “father of modern analysis”. However, the university senate would not let Sofia attend university, even with the support of her teachers. Over the next four years Weierstrass tutored her privately.
Three years later, she presented three papers to the Göttingen as her doctoral dissertation:
- on partial differential equations,
- on the dynamics of Saturn’s rings
- and on elliptic integrals.
With the invaluable support of Karl Weierstrass, this earned her a doctorate in mathematics summa cum laude, bypassing the usual required lectures and examinations. She became the first woman in Europe to hold that degree.
Sadly, Sofia and Vladimir now developed financial problems. Sofia wanted to work as a lecturer at the university; however, she was not allowed to because she was a woman, and this was despite volunteering to provide free lectures as proof of her abilities. At this point, her relationship with Vladimir changed. They had a daughter together. However, Sofia was not happy as a wife and mother, so she left Vladimir, and arranged for her sister to care for their daughter while she returned to her first love, Mathematics.
Alas, Vladimir, never the strongest of personalities, beset with financial woes, and now separated from Sofia for two years and bereft of her emotional support, committed suicide. He had made some sound contributions to science, supporting and translating Darwin’s works, as well as supporting Sofia’s battles to get an education. Sofia was saddened his death. She went on to have a relationship with her late husband’s cousin, Maksim Maksimovich Kovalevsky, a socialologist; they never formalised the relationship but they remained lovers for the rest of Sofia’s life. Some historians have suggested she also had a romantic relationship with her friend, Anne Charlotte Edgren-Leffler. Sofia did not live a life without love.
After Vladamir’s death, Sofia Kovalevskaya accepted Magnus Gösta Mittag-Leffler’s invitation to become a lecturer in mathematics at the University of Stockholm (he was Anne’s brother). She was promoted to full professor in 1889. In 1884 she joined the editorial board of the mathematical journal Acta Mathematica, and in 1888 she became the first woman to be elected a corresponding member of the Russian Academy of Sciences. In 1888, she was awarded the Prix Bordin of the French Academy of Sciences for a paper on the rotation of a solid body around a fixed point. And then, in 1889, she was appointed Professor Ordinarius at Stockholm University, the first woman to hold such a position at a northern European university. After much lobbying on her behalf (and a change in the Academy’s rules) she was granted a Chair in the Russian Academy of Sciences, but was never offered a professorship in Russia.
During this latter period of her life, Sofia gained a reputation as a writer, an advocate of women’s rights, and a champion of radical political causes. She composed novels, plays, and essays, including the autobiographical Memories of Childhood and The Nihilist Woman, a depiction of her life in Russia. She had only managed to publish ten scientific papers before her death from influenza, complicated with pneumonia, after a trip to Paris to see Maksim. She was only forty-one, but she had packed a lot of living into her short life.
Sofia didn’t let anything discourage her from her goals. Imagine what she might have achieved if she had lived to be eighty.