Sophia Vasilevna Kovalevsky

Sophia Kovalevsky (1850-1891) was the first woman to earn a Ph.D. in mathematics, despite the fact that Russia, her native country, and many other European universities at that time did not allow women. Kovalevsky was inspired by the nihilist movement in Russia, which emphasized the power of education and the equality of women. Kovalevsky was also an accomplished writer and a strong proponent of higher education for women.

Family Life

Sophia Korvin-Krukovsky was born on January 15, 1850, in Moscow to Vasily Vasilevich Korvin-Krukovsky, a general in the artillery garrison of the Russian army, and Elizabeth Fedrovna. She was the second child born to the couple; her sister, Anna, was six years older. Five years after her birth, her brother, Fedor, was born. Sophia was raised primarily by a serf nurse named Praskovia. As a child she was nicknamed "Little Sparrow" because she was small and energetic.

When Sophia was eight years old her father, then 59, resigned his commission in the army and moved the family to his country estate in Palibino. At this time he also hired a Polish tutor, Iosif Ignatevich Matevich, and an English governess, Margarita Frantsevna Smith, to supervise his children. In her memoir, Kovalevsky portrays herself as a sad and lonely child who felt unloved. Her sister garnered much attention for being the oldest and her brother was the pride of his parents because he was the only son. However, she eventually developed a special bond with her father and became his favorite child when her intellectual potential became apparent.

Sophia was also close to her father's older brother, Petr Vasilevich Korvin-Krukovsky. He was a well-read man who shared with his niece his political views and knowledge on various subjects, including mathematics. Her introduction to advanced mathematics came as an accident. When the Korvin-Krukovsky family moved to Palibino, they re-decorated their home. When they ran out of wallpaper for the nursery, her father used sheets of old school notes instead. The notes were on differential integral analysis and were her first encounter with calculus.

Early Education

Sophia struggled against social conventions to get a proper education as a child. Though it was then believed that very young children should not be taught to read, she sat in on her sister's lessons and practiced reading by herself. When her governess limited the number and types of books she was allowed, she sneaked into her father's study to read from his collection. Her formal education was the responsibility of the family tutor, Malevich. He taught her a broad range of subjects from age the time she was 8 until she was 17. She excelled in mathematics. When her father realized this, he instructed her to focus on other subjects. She followed his orders during her tutoring time, but continued to read math books alone at night.

Sophia was allowed to continue her formal mathematics training after she impressed a neighbor with her skills. The neighbor was Nikolai Nikanorovich Tyrtov, a professor of physics at the St. Petersburg Naval Academy. He brought the Korvin-Krukovsky family a copy of a beginning physics textbook as a gift, and she immediately began to read it. She had difficulty understanding it at first because it contained trigonometry, and Malevich was unable to explain the advanced math to her. Through perseverance Sophia figured out the mathematical formulae by herself and finished the book. Tyrtov was impressed by her ability to explain how she figured out the trigonometry. Tyrtov was a strong proponent of higher education for women, and he eventually persuaded the general to allow his daughter to pursue an education in mathematics.

When Sophia was 18, her family moved to St. Petersburg in order to get a better education for her and her brother. Her father hired Alexander Nikolayevich Strannoliubsky, a highly accomplished teacher, as a math tutor. Her remarkable mathematical abilities persuaded Strannoliubsky to become actively involved in promoting women's education in Russia. Eventually he encouraged her to pursue a broader university education. However, Russian universities were closed to women and unmarried women were not allowed to travel abroad, even to study, unless accompanied by a chaperone.

Nihilist Influences

While Sophia was pursuing her scientific interests, her older sister was developing her literary talents and political views, both of which later influenced Sophia's life. Anna began writing as a pastime but eventually secretly published two short stories without her father's permission in a literary journal edited by Fedor and Mikhail Dostoevsky. This led to a brief courtship between Anna and the famous novelist Fedor Dostoevsky, whom Sophia was also very fond of. Anna also became involved in the nihilist movement in Russia. As Koblitz explained in A Convergence of Lives, a nihilist "basically denoted a person who questioned just about everything in traditional tsarist Russia, had great faith in the natural sciences and the power of education, strongly believed in the equality of women, and desired to be of use to the common people in some capacity." Anna's political views influenced her sister, who saw this movement as a means to pursue her education. The sisters decided that the only way to further their education would be for one of them to marry so they could both travel abroad. They planned a "fictitious marriage" whereby a man would agree to the marriage ceremony, but would then let the woman pursue her own life. This was not an unusual arrangement at the time since it was the only way to free a woman from her parents' authority.

The sisters decided that Anna should partake in the fictitious marriage since she was older. However, when the intended husband, nihilist Vladimir Onufrievich Kovalevsky, a publisher of political and scientific works, met the sisters, he was more interested in Sophia because of her intellectual achievements. The couple married in September 1868 and settled in St. Petersburg. Sophia Kovalevsky continued her math lessons with Strannoliubsky but also sat in on classes at the Medical-Surgical Academy. There she befriended a woman who had started her own gynecological practice, and Kovalevsky briefly entertained the idea of a career in medicine. However, she soon realized that mathematics was her true passion.

Pursuit of Higher Education

In order for Kovalevsky to pursue a formal education in mathematics, the newlyweds first moved to Vienna. Kovalevsky was allowed to study physics there, but she could not find a math professor to work with her, so the couple moved to Heidelberg. There, Kovalevsky was allowed to take math courses as well as a variety of other subjects, and her husband studied geology and paleontology. During this time the couple traveled extensively and had social contacts with the leading intellectuals of that time, including Charles Darwin, Thomas Huxley, George Elliot, and Herbert Spencer.

The Kovalevskys soon left Heidelberg to pursue their separate educations. Vladimir moved to Vienna, while Sophia went to Berlin to study with the world-renowned mathematician, Karl Theodore Weierstrass. Weierstrass was reluctant to take Kovalevsky as a student and gave her a test with difficult math problems before agreeing to work with her. He was so impressed by her performance on his test that he tried to get her admitted to the university. He was not successful, so Weierstrass tutored her privately for the next four years. At first he did not consider the possibility of preparing her for a doctorate because he did not believe that married women needed a career. However, when he learned the truth about Kovalevsky's marriage, he changed his mind.

Kovalevsky worked on three doctoral theses under Weierstrass's guidance and applied to the University of Gottingen, which allowed foreigners to obtain degrees in abstentia. Her first paper, and most significant contribution to mathematics, was on the theory of partial differential equations. It was published in Crulle's Journal, which was a major accomplishment for a young academic. Her second paper, in theoretical astronomy, was about the form of Saturn's rings, and the third paper explained how to reduce certain integrals to less complicated forms. Her papers were accepted at Gottingen and were so remarkable that she was excused from taking the final oral examination. She received her Ph.D. in mathematics, summa cum laude, in August 1874. Kovalevsky was the first woman to obtain a doctorate in this field.

Two years earlier Vladimir Kovalevsky completed his dissertation in paleontology from Jena University in Germany. In 1874 Kovalevsky and her husband reunited and returned to Russia in search of academic positions. Neither was successful, so Vladimir got involved with some business ventures and Sophia began writing for a newspaper as a theater critic and became a public supporter of women's higher education. As Kovalevsky explained in A Russian Childhood, "Various circumstances existed in Russia which distracted me from serious scientific work: society itself, and those conditions under which one had to live." The couple's marriage became stronger and they decided to have a child together. In October 1878 their daughter, Sophia Vladimirovna, was born. For the next two years Kovalevsky concentrated on her new family instead of mathematics.

International Recognition

In 1880 a colleague of the Kovalevskys invited Sophia to present a paper at the Sixth Congress of Natural Scientists in Petersburg. Since Kovalevsky had not done any mathematical work in six years, she presented one of her dissertations from Gottingen. The response was very positive, and colleagues persuaded Kovalevsky to return to academia. She traveled to Berlin and Paris to reunite with Weierstrass and conduct research on the refraction of light in crystals. During this time her husband's financial enterprises failed. Vladimir had been suffering from depression, and when his next job opportunity also fell through he committed suicide.

Kovalevsky was devastated by her husband's death. In 1883 a colleague offered Kovalevsky a teaching position at Stockholm University. After only a year, she was appointed to full professor and published her research on light refraction. In 1885 Kovalevsky was appointed chair of mechanics. Throughout her life Kovalevsky was also very interested in literature and now she decided to pursue it more seriously. She co-authored a play called A Struggle for Happiness with Anne Charlotte Leffler. The play was not well received, but Kovalevsky did not give up writing. She wrote some novels, radical political books such as A Nihilist Girl, and her memoirs.

Mathematics remained her main passion. In 1888 she won the prestigious Prix Bordin competition sponsored by the French Academy of Science. Her brilliant career was cut short, however, when she died on February 10, 1891, of pneumonia at age 41. Kovalevsky's legacy lies not only in her accomplishments as a mathematician, but also in the recognition and respect that she brought women in academia and her efforts to support women pursuing a higher education.

Books

Cooke, Roger, The Mathematics of Sonya Kovalevskaya, Springer-Verlag, 1984.

Kennedy, Don H., Little Sparrow: A Portrait of Sophia Kovalevsky, Ohio University Press, 1983.

Koblitz, Ann Hubner, A Convergence of Lives. Sofia Kovalevskaia: Scientist, Writer, Revolutionary, Rutgers University Press, 1993.

Kochina, Pelageya, Love and Mathematics: Sofya Kovalevskaya, Mir Publishers, 1985.

Kovalevskaya, Sofya, A Russian Childhood, Springer-Verlag, 1978.

Leffler, Ana Carlotta, Sonia Kovalevaky, MacMillan and Co., 1895.

Periodicals

Natural History, June 1996.

Online

"Engines of Our Ingenuity No. 225: Sonya Kovalevsky," University of Houston,http://www.uh.edu/engines/epi225.html (January 11, 2002).

"The Queen of PDE's," Women in Math,http://www.mathnews.uwaterloo.ca/Bestof/WomenInMath6904.html (January 11, 2002).

"Sofia Vasilevna Kovalevskaia (1850-1891)," American University,http://www.american.edu/academic.depts/cas/mathstat/skday01/BIO-SK.html (January 11, 2002).

"Sofia Vasilevna Kovalevskaya," University of St. Andrews,http://www-groups.dcs.st-andrews.ac.uk/~history/Miscellaneous/Kovalevskaya/biog.html (January 11, 2002).

"Sonya Kovalevsky," Bellevue Community College,http://www.scidiv.bcc.ctc.edu/Math/Kovalevsky.html (January 11, 2002).

"Sophia Kovalevskaya," Agnes Scott College,http://www.agnesscott.edu/lriddle/women/kova.html (January 10, 2002). □