An extraordinary woman, Sofia Kovalevskaya was not only a great mathematician, but also a writer and advocate of women's rights in the 19th century. It was her struggle to obtain the best education available which began to open doors at universities to women. In addition, her ground-breaking work in mathematics made her male counterparts reconsider their archaic notions of women's inferiority to men in such scientific arenas.
Sofia Krukovsky Kovalevskaya was born in 1850. As the child of a Russian family of minor nobility, Sofia was raised in plush surroundings. She was not a typically happy child, though. She felt very neglected as the middle child in the family of a well admired, first-born daughter, Anya, and of the younger male heir, Fedya. For much of her childhood she was also under the care of a very strict governess who made it her personal duty to turn Sofia into a young lady. As a result, Sofia became fairly nervous and withdrawn--traits which were evident throughout her lifetime (Perl 127-128).
Sofia's exposure to mathematics began at a very young age. She claims to have studied her father's old calculus notes that were papered on her nursery wall in replacement for a shortage of wallpaper. Sofia credits her uncle Peter for first sparking her curiosity in mathematics. He took an interest in Sofia and made time to discuss numerous abstractions and mathematical concepts with her (Rappaport 564). When she was fourteen years old she taught herself trigonometry in order to understand the optics section of a physics book that she was reading. The author of the book and also her neighbor, Professor Tyrtov, was extremely impressed with her capabilities and convinced her father to allow her to go off to school in St. Petersburg to continue her studies (Rappaport 564).
After concluding her secondary schooling, Sofia was determined to continue her education at the university level. However, the closest universities open to women were in Switzerland, and young, unmarried women were not permitted to travel alone. To resolve the problem Sofia entered into a marriage of convenience to Vladimir Kovalevsky in September 1868. The couple remained in Petersburg for the first few months of their marriage and then traveled to Heidelburg where Sofia gained a small fame. People were enthralled by the quiet Russian girl with an outstanding academic reputation (Perl 131).
In 1870, Sofia decided that she wanted to pursue studies under Karl Weierstrass at the University of Berlin. Weierstrass was considered one of the most renowned mathematicians of his time, and at first he did not take Sofia seriously. Only after evaluating a problem set he had given her did he realize the genius at his hands. He immediately set to work privately tutoring her because the university still would not permit women to attend. Sofia studied under Weierstrass for four years. She is quoted as having said, "These studies had the deepest possible influence on my entire career in mathematics. They determined finally and irrevocably the direction I was to follow in my later scientific work: all my work has been done precisely in the spirit of Weierstrass" (Rappaport 566). At the end of her four years she had produced three papers in the hopes of being awarded a degree. 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 566).
In July of 1874, Sofia Kovalevskaya was granted a Ph.D. from the University of Gottingen. 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 133). 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 567).
In 1880, 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 134).
Then, in 1883, 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 1885, was also appointed Chair of Mechanics. At the same time, she co-wrote a play, "The Struggle for Happiness," with friend, Anna Leffler (Rappaport 568).
In 1887, Sofia again received devastating news. The death of her sister, Anya, was particularly hard on Sofia because the two had always been very close. Fortunately, it was not long afterward that Sofia achieved "her greatest personal triumph" (Perl 135). In 1888, she entered her paper, "On the Rotation of a Solid Body about a Fixed Point," in a competition for the Prix Bordin by the French Academy of Science and won. "Prior to Sofya Kovalevsky's [Sofia Kovalevskaya] work the only solutions to the motion of a rigid body about a fixed point had been developed for the two cases where the body is symmetric" (Rappaort 569). In her paper, Sofia developed the theory for an unsymmetrical body where the center of its mass is not on an axis in the body. The paper was so highly regarded that the prize money was increased from 3000 to 5000 francs.
Also at this time, a new man entered her life. Maxim Kovalevsky came to Stockholm for a series of lectures. There he met Sofia, and the two had a scandalous, rocky affair. The basic problem was that they were both too passionate about their work to give it up for the other. Maxim's work took him away from Stockholm and he wanted Sofia to give up her hard-earned positions to simply be his wife. Sofia flatly rejected such an idea but still could not bear the loss of him. She remained in France with him for the summer and fell into another one of her frequent depressions. Again, she turned to her writing. While she was in France, she finished Recollections of Childhood (Perl 136).
In the fall of 1889, she returned to Stockholm. She was still miserable at the loss of Maxim even though she frequently traveled to France to visit him. She eventually became ill with depression and pneumonia. On February 10, 1891, Sofia Kovalevskaya died and the scientific world mourned her loss. During her career she published ten papers in mathematics and mathematical physics and also several literary works. Many of these scientific papers were ground-breaking theories or the impetus for future discoveries. There is no question that Sofia Krukovsky Kovalevskaya was an incredible person. The President of the Academy of Sciences, which awarded Sofia the Prix Bordin, once said: "Our co-members have found that her work bears witness not only to profound and broad knowledge, but to a mind of great inventiveness" (Rappaort 569).
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