Shortly after, Vladimir got a job offer and Sofia helped neighbors to electrify street lights. Vladimir and Sofia quickly established themselves again financially. The Kovalevskys returned to Russia, but failed to secure professorships because of their radical political beliefs. Discouraged, they went back to Germany. Vladimir, who had always suffered severe mood swings, became more unstable so they spent most of their time apart.
Then, for some unknown reason, they decided to spend several years together as an actual married couple. During this time their daughter, Sofia called "Fufa" , was born. After a year devoted to raising her daughter, Kovalevskaya put Fufa under the care of her older sister, resumed her work in mathematics and left Vladimir for what would be the last time. In , faced with worsening mood swings and the possibility of being prosecuted for his role in a stock swindle, Vladimir committed suicide.
Until Kovalevsky's death the two women shared a close friendship. The following year she was appointed to a five year position as "Professor Extraordinarius" Professor without Chair and became the editor of Acta Mathematica.
Her submission included the celebrated discovery of what is now known as the "Kovalevsky top", which was subsequently shown by Liouville to be the only other case of rigid body motion, beside the tops of Euler and Lagrange, that is "completely integrable". We need to also say a little about Sofia Kovalevskaya's name.
She was given the name Sofia Vasilievna Krukovsky, only adopting the name Korvin-Krukovsky after her father's application for nobility was accepted in She is often called Sophie or Sonya, the first being an anglicised version of Sofia, the second being a familiar version by which she was known by her friends after she became an adult.
Kovalevskaya is the female version of her husband's name Kovalevsky which is often transliterated as Kovalevskaia, and infrequently as Kovalevskaja. She is also known as Sonya Kovalevsky, using a masculine version of her surname, a form she sometimes used herself.
We will use the form Sofia Kovalevskaya throughout this biography. In Sofia's father, General Krukovsky, was posted to Kaluga, about 70 km south west of Moscow, and the family lived there until The family had a nanny and a governess for Anyuta who was twelve years old when they moved to Kaluga. Sofia lived at Palibino, the Krukovsky country estate, from when he father retired, and was educated by tutors and governesses. Palibino was near the Lithuanian border and was a large estate with sheep and cattle, lakes stocked with fish, forests with game, and vegetable gardens.
Sofia's father was fully occupied managing the estate and the family lived comfortably in the manor house. It was at a very young age that Sofia was attracted to mathematics. Her uncle Pyotr Vasilievich Krukovsky, her father's elder brother, often visited Palabino.
She writes about him in [ 62 ] :- Although he was the oldest member of our family and should have been its head, the truth was that he was ordered about by anyone who felt like it, and the whole family treated him like an elderly child. He had long held the reputation of an eccentric and a dreamer. His wife had died some years before; he had handed over his entire and rather good-sized estate to his only son, leaving for himself only a very small monthly pension.
Left thus without any definite business affairs to attend to, he used to come to Palibino often and stayed with us for weeks on end. His arrival was always regarded as a holiday, and the atmosphere at home became somehow livelier and cosier when he was with us.
Uncle Pyotr Vasilievich had a great respect for mathematics and often spoke about the subject. Sofia wrote in her autobiography [ 62 ] :- The meaning of these concepts I naturally could not yet grasp, but they acted on my imagination, instilling in me a reverence for mathematics as an exalted and mysterious science which opens up to its initiates a new world of wonders, inaccessible to ordinary mortals.
When Sofia was 11 years old, the walls of her nursery were papered with pages of Ostrogradski 's lecture notes on differential and integral analysis. This requires some explanation! Before the family moved from Kaluga to Palibino, they had the whole manor house redecorated. Wallpaper was ordered from St Petersburg but they had made a small error in working out how many rolls would be required and ended up one short.
Rather than order one roll, they decided to paper the nursery with old sheets of paper and looked for some in their attic. Ostrogradski 's lecture notes on differential and integral analysis were there because Vasily Vasilievich, Sofia's father, had attended his course when undergoing his military training. She noticed that there were certain things on the sheets she had heard mentioned by her uncle.
Studying the wallpaper was Sofia's introduction to calculus. It was under the family's tutor, Yosif Ignatievich Malevich - , that Sofia undertook her first proper study of mathematics, beginning with arithmetic which she found boring and then moving on to elementary geometry and algebra. She writes that it was as his pupil that [ 62 ] :- I began to feel an attraction for my mathematics so intense that I started to neglect my other studies.
Sofia's father decided to put a stop to her mathematics lessons but she borrowed a copy of Bourdon's Algebra Course which she read at night when the rest of the household was asleep [ 62 ] :- Since I was under my governess's strict surveillance all day long, I was forced to practice some cunning in this matter. At bedtime I used to put the book under my pillow and then, when everyone was asleep, I would read the night through under the dim light of the icon-lamp or the night lamp.
Under such circumstances, of course, I did not dare dream of continuing the systematic study of my favourite subject. My mathematical knowledge would likely have remained confined for a long time, to the contents of Bourdon's 'Algebra' if I had not been aided by the following incident, which motivated my father to reassess his views on my education to some degree.
The incident she refers to happened a year later when a neighbour, Nikolai Tyrtov, Professor of Physics at the Naval Academy, presented her family with a physics textbook which he had written, and Sofia attempted to read it.
She did not understand the trigonometric formulae that she came across in the chapter on optics and attempted to explain them herself. Tyrtov realised that in her working with the concept of sine, she had used the same method by which it had been developed historically.
Tyrtov argued with Sofia's father that she should be encouraged to study mathematics further but it was two years later before he permitted Sofia to take private lessons with Aleksandr Strannoliubskii - who had been a student of Tyrtov. These lessons on analytic geometry, and differential and integral calculus, took place when the family were in St Petersburg, where they spent some time each year visiting the Shubert aunts.
There Sofia joined her family's social circle which included the author Fyodor Mikhailovich Dostoevsky. We now need to say a little about Sofia's sister Anyuta at this point, because she was a strong influence on the young Sofia.
In around Anyuta had become enthusiastic about the radical ideas that one of her friends, the son of the local priest, told her about when he was home in Palibino from his university studies during the vacation.
Anyuta wanted to go to St Petersburg to live, and even proposed living in a commune where young people were living together without servants. Her father was not going to allow such behaviour and Anyuta had to remain at Palibino. She reacted by secretly writing and getting two pieces published under a male pseudonym. Well, it was done secretly from everyone except Sofia, for the two sisters kept nothing from each other.
On 28 February the family went to St Petersburg. Dostoevsky came to visit and both Anyuta and Sofia would meet him. Usually they were not allowed to be alone with him but on one occasion their parents were out and the three were able to chat together. The first of these, "On the Theory of Partial Differential Equations," was even published in Crelle's journal, a tremendous honor for an unknown mathematician Rappaport In July of , Sofia Kovalevskaya was granted a Ph.
Yet even with such a prestigious degree and the help of Weierstrass, who had grown quite fond of his pupil, she was not able to find employment. She and Vladimir decided to return to her family in Palobino. Shortly after her return home, her father died unexpectedly. It was during this period of sorrow that Sofia and Vladimir fell in love.
Their marriage produced one daughter Perl While at home, Sofia neglected her work in mathematics but instead developed her literary skills. She tried her hand at fiction, theater reviews, and science articles for a newspaper Rappaport In , Sofia returned to her work in mathematics with a new fervor. She presented a paper on Abelian integrals at a scientific conference and was very well received.
Once again she was faced with the dilemma of finding employment doing what she loved most--mathematics. She decided to return to Berlin, also home to Weierstrass.
She was not there long before she learned of Vladimir's death. He had committed suicide when all of his business ventures had collapsed.
Sofia's grief threw her into her work more passionately than ever Perl Then, in , Sofia's luck took a turn for the better. She received an invitation from an acquaintance and former student of Weierstrass, Gosta Mittag-Leffler, to lecture at the University of Stockholm. In the beginning it was only a temporary position, but at the end of a five year period, Sofia had more than proven her value to the university.
Then came a series of great accomplishments. She gained a tenured position at the university, was appointed an editor for a mathematics journal, published her first paper on crystals, and in , was also appointed Chair of Mechanics.
Designed by: Rosemarie Dias References. Kennedy, D. Athens: Ohio University Press. Koblitz, A. A Convergence of Lives: Sofia Kovalevskaia, a scientist, writer, revolutionary. Boston: Burkhauser.
Osen, L. Women in Mathematics.
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