Sofya Kovalevskaya

Russian mathematician

• Born: January 15, 1850
• Birthplace: Moscow, Russia
• Died: February 10, 1891
• Place of death: Stockholm, Sweden

Kovalevskaya was the first woman in the world to receive a doctorate in mathematics from a European university and was also the first woman to teach at a European university during the nineteenth century. Her achievements in mathematics provided evidence of the ability of women to conduct research at the highest level and were recognized throughout Europe.

Early Life

Sofya Kovalevskaya (kah-vah-LYAYF-skah-yah) was born Sofya Korvin-Krukovskaya. Her family had an estate located near the borders of what are now Russia, Lithuania, and Belarus; was affluent; and had a tradition of education. Her mother had German roots; her mother’s maiden name was Schubert, and her mother’s grandfather had been a German mathematician and astronomer.

Sofya’s mother had inherited her grandfather’s concern for education, and Sofya herself enjoyed the attention of a sequence of governesses of various nationalities, none of them Russian. This was in accord with the attitude of the educated Russian class of the time, who saw the benefit in exposing children to cultures and languages other than their own. As a result, Sofya was able to read in English and French from an early age and made good use of her language skills.

Sofya also displayed an early interest in mathematics, supposedly linked to the fact that copies of lectures given by a distinguished Russian mathematician were used to paper the wall of a bedroom. One of her uncles stimulated her interest in the subject, and she taught herself trigonometry. Her interests also extended to other sciences, and she used a microscope she purchased herself to study biology. Within her home there was no limit to the extent to which she could pursue intellectual interests. However, in the wider world, it was a different story.

The University of St. Petersburg had opened its lecture halls to women in 1861, when Sofya was eleven, but subsequent agitation led to government crackdowns and the withdrawal of the privilege for women to attend. As a result, it was clear that Sofya would have to go abroad if she wanted to pursue the various studies to which she was attracted. The difficulty was that unmarried Russian women were not allowed to travel abroad on their own. The standard solution was for women who were interested in studying elsewhere to enter into marriages of convenience with men willing to support their endeavors without necessarily expecting anything more from their marriages.

The man who played the appropriate role in Sofya’s life was Vladimir Kovalevskii, an individual with scientific interests as well as political ones. There was a definite political slant to the intellectual circles in which the two spent their time, usually characterized by the term “nihilist.” That term, which came from the attitudes of a character in Ivan Turgenev’s novel Fathers and Sons (1862), summarized the view of a generation of intellectuals who found unpersuasive the extensive rules governing life and political action in the old Russian Empire. Instead, they wanted to start over again without regard for rank and wealth. Not surprisingly, this attitude was not encouraged by the government, and ongoing battles between nihilists and government agents provided another reason for going abroad.

After Sofya married Kovalevskii in September, 1868, she went abroad to study mathematics. She and her husband were also eager to find an interesting political circle, so they went first to Vienna, Austria, and then to England. Neither place fully met their needs, so by the end of the summer of 1869 they had gone to Heidelberg, Germany. Kovalevskii studied paleontology there but decided to finish his degree at the University of Jena, another German institution. Sofya, meanwhile, had decided to go the fountainhead of mathematics to study at the University of Berlin under the eminent mathematician Karl Weierstrass. Sofya’s separation from her husband was to be typical of much of the couple’s marriage, which ended when Kovalevskii committed suicide in 1883.

Life’s Work

The prestigious position that Weierstrass held in the world of German mathematics gave him opportunities to do things that lesser scholars would not have been permitted to do; however, even he could not manage to arrange for Kovalevskaya to get credit for the work that she did with him. It was difficult for him simply to get her permission to use the university library. While the general political atmosphere in Berlin might have been more liberal than it was in Russia, that did not mean that Berlin provided a comfortable environment for a woman to make academic progress. There existed a tendency to discount the mathematical achievements of women—especially women as physically attractive as Kovalevskaya—and to attribute any success they demonstrated to their borrowing the work of their male colleagues. One indication of the stature of both Weierstrass and Kovalevskaya is the fact that no whisper of such claims was ever made about Kovalevskaya’s work.

The work for which Kovalevskaya was to become best known pertained to the study of partial differential equations, which govern the behavior of most physical processes and describe how certain quantities change with changes in other quantities, such as time and position. Solutions to such equations raised great difficulties, but Kovalevskaya was able to apply Weierstrass’s ideas to build a theoretical foundation for the subject, while looking for solutions. Meanwhile, she earned a doctoral degree from the University of Göttingen; she received it in absentia, which was a means of avoiding the issue of her being a woman. Although women had previously earned reputations in Europe as mathematicians, Kovalevskaya was the first woman to get a doctorate, a degree whose importance in the research arena was of relatively recent creation.

When Kovalevskaya returned to Russia and her husband, she looked for a suitable job but found opportunities at the university level and academies of science limited—partly because of her unpopular political views. In 1878, she gave birth to the only child she had by her husband. Two years later, she returned to Berlin. From there she hoped to be able to find a position in mathematics in some other country, but even Weierstrass’s recommendation was not enough for some institutions. For example, the University of Helsinki did not offer her a position for which she was well qualified, but it is unclear whether being a Russian or being a woman was considered the greater disqualification in Finland.

In 1884, Kovalevskaya finally received a position in Stockholm, thanks to the efforts of the mathematician Gosta Mittag-Leffler, who had been so impressed by her work that he had traveled to St. Petersburg to hear her speak before she returned to Berlin. Mittag-Leffler arranged for Kovalevskaya to get a salaried five-year professorship after she had proven her mathematical skills during her first year in Stockholm. Her responsibilities in Stockholm included lecturing and tutoring, as well as carrying out research in collaboration with Mittag-Leffler.

Even at that stage in Kovalevskaya’s career, she was not allowed to attend lectures in Berlin, a tribute to the continuing difficulties with which women mathematicians had to contend in Europe. It is also true that the distinguished Swedish playwright August Strindberg was openly negative about Kovalevskaya’s presence on the faculty in Stockholm, although he was scarcely qualified to criticize her mathematical work.

Despite the efforts of Mittag-Leffler to make her feel at home, Kovalevskaya became bored with Stockholm. Her stock in the mathematical world rose considerably when she received the Borodin Prize of the French Academy of Sciences in 1888 for her solution of a problem about the motion of a rigid body rotating about a fixed point. The subject had been under investigation for some time, and Kovalevskaya was far from the only entrant in the competition for the prize. It was a measure of her success that the academy doubled its cash award to her in recognition of the elegance of her solution. On the strength of this award, Kovalevskaya hoped that she could find an academic post in Paris or Russia.

Kovalevskaya’s quest for alternative employment proved unavailing, but the Russian mathematician Pafnuty Chebyshev succeeded in having her named the first woman corresponding member of Russia’s Imperial Academy of Sciences. In 1891, she taught the first classes of the spring semester in Stockholm but died shortly afterward.

Significance

At the time of her death, Sofya Kovalevskaya was best known to the general public in Russia for her writings, especially an autobiographical account of her childhood. The mathematical community recognized her for her ability to carry on the research program of Weierstrass as applied to a variety of particular problems.

On one hand, Kovalevskaya was a mathematician whose work need not fear comparison with that of any of her contemporaries. She was educated in the best style of Weierstrassian analysis, and she made contributions to the study of partial differential equations in the form of textbooks and research articles. Those attacking more general problems involving rotations were able to build on her efforts.

On the other hand, there is no doubt that Kovalevskaya’s life has received a great deal of attention because she was the first woman to do much of what she accomplished. She certainly did not enjoy having to overcome the difficulties placed in the way of women trying to do research in mathematics, and the intervals in her life when she stopped doing mathematics are representative of her own ambivalence. Nevertheless, the success that she achieved despite the handicaps enabled women following after to point to her distinguished precedent. During the late twentieth century a Kovalevskaya Fund was set up in her honor to help support the educational efforts of women in the sciences in underdeveloped countries. Her political and scientific testament could not have been better expressed.

Bibliography

Cooke, Roger. The Mathematics of Sonya Kovalevskaya. New York: Springer-Verlag, 1984. The most extensive analysis of Kovaleskaya’s mathematics, tracing its historical roots from the work of Weierstrass and his predecessors.

James, Ioan. Remarkable Mathematicians. Cambridge, England: Cambridge University Press, 2002. The sketch of Kovalevskaya does not go into detail about her mathematics but spells out some of the mathematical connections that she built during her career.

Kennedy, Don H. Little Sparrow: A Portrait of Sophia Kovalevsky. Athens: Ohio University Press, 1983. A political and literary biography that steers away from mathematics.

Koblitz, Ann Hibner. A Convergence of Lives. 2d ed. New Brunswick, N.J.: Rutgers University Press, 1993. One of the books that started a revival of interest in Kovalevskaya’s work in English, paying attention to her literary, political, and scientific careers.

Kovalevskaya, Sofya. A Russian Childhood. Translated and introduced by Beatrice Stillman. New York: Springer-Verlag, 1978. The autobiography that won Kovalevskaya the most recognition in her lifetime, translated into modern English. Contains an analysis of her mathematics by P. Y. Kochina.

Spicci, Joan. Beyond the Limit: The Dream of Sofya Kovalevskaya. New York: Forge Press, 2002. Although well researched, this biography borders on fiction and traces Kovalevskaya’s career only up to the moment that she earned her doctorate in 1874.