Sofya Vasilyevna Kovalevskaya (; born Korvin-Krukovskaya; – 10 February 1891) was a Russian mathematician who made noteworthy contributions to analysis, partial differential equations and mechanics. She was a pioneer of equality for women in mathematics. Kovalevskaya was the first woman to earn a doctorate in mathematics, in the modern sense of that term, the first woman in Europe in modern times appointed to a full professorship in mathematics, as well as one of the first women to work for a scientific journal as an editor. According to historian of science Ann Hibner Koblitz, Kovalevskaya was "the greatest known woman scientist before the twentieth century".
Historian of mathematics Roger Cooke writes:
There are several alternative transliterations of her name. She herself used Sophie Kowalevski (or occasionally Kowalevsky) in her academic publications. In Sweden she was known as Sonja Kovalevsky; Sonja (Russian: ) is her Russian nickname.
Background and early education
Sofya Kovalevskaya (née Korvin-Krukovskaya) was born in Moscow, the second of three children. Her sister was the socialist Anne Jaclard and they had a brother called Fedya. Kovalevskaya's father, Lieutenant General , served in the Imperial Russian Army as head of the Moscow Artillery before retiring to Polibino, his family estate in Pskov Oblast in 1858, when Kovalevskaya was eight years old. He was a member of the minor Russian nobility, of mixed Belarusian–Polish descent (Polish on his father's side), with possible partial ancestry from the royal Corvin family of Hungary, and served as Marshall of Nobility for Vitebsk province. (There may also have been some Romani ancestry on the father's side.)
Her mother, Yelizaveta Fedorovna von Schubert (1820–1879), descended from a family of German immigrants to St. Petersburg who lived on Vasilievsky Island. Her maternal great-grandfather was the astronomer and geographer Friedrich Theodor von Schubert (1758–1825), who emigrated to Russia from Germany around 1785. He became a full member of the St. Petersburg Academy of Science and head of its astronomical observatory. His son, Kovalevskaya's maternal grandfather, was General Theodor Friedrich von Schubert (1789–1865), who was head of the military topographic service, and an honorary member of the Russian Academy of Sciences, as well as Director of the Kunstkamera museum.
Kovalevskaya's parents provided her with a good early education. At various times, her governesses were native speakers of English, French, and German. When she was 11 years old, she was intrigued by a foretaste of what she was to learn later in her lessons in calculus; the wall of her room had been papered with pages from lecture notes by Mikhail Ostrogradsky on differential and integral calculus, left over from her father's student days, as not enough wallpaper had been ordered to cover the walls of all of the children's rooms. She was tutored privately in elementary mathematics by Iosif Ignatevich Malevich.
The physicist Nikolai Nikanorovich Tyrtov noted Kovalevskaya's unusual aptitude when she managed to understand his textbook by discovering for herself an approximate construction of trigonometric functions which she had not yet encountered in her studies.Korvin-Krukovskii, F. V. (1891) "Sofia Vasilevna Korvin-Krukovskaia," Russkaia Starina, 71 (9), p. 623-636. Tyrtov called her a "new Pascal" and suggested she be given a chance to pursue further studies under the tutelage of .Rappaport, Karen D. (October 1981) "S. Kovalevsky: A Mathematical Lesson." The American Mathematical Monthly 88 (8): 564–573. Mathematical Association of America. In 1866–67 she spent much of the winter with her family in St. Petersburg, where she was provided private tutoring by Strannoliubskii, a well-known advocate of higher education for women, who taught her calculus. During that same period, the son of a local priest introduced her sister Anna to progressive ideas influenced by the radical movement of the 1860s, providing her with copies of radical journals of the time discussing Russian nihilism.Kovalevskaya, Sofya. A Russian Childhood, translated, edited, and introduced by Beatrice Stillman; with an analysis of Kovalevskaya's Mathematics by Pelageya Polubarinova-Kochina. Springer-Verlag, c. 1978
Although the word nihilist (нигилист) often was used in a negative sense, it did not have that meaning for the young Russians of the 1860s (шестидесятники):
Despite her obvious talent for mathematics, Kovalevskaya could not complete her education in Russia. At that time, women were not allowed to attend universities in Russia and most other countries. In order to study abroad, Kovalevskaya needed written permission from her father (or husband). According to Kovalevskaya's close friend Elizaveta Litvinova, Kovalevskaya could have convinced her father to let her go abroad for advanced study, but preferred a fictitious marriage because it was more dramatic and was fashionable among the radicals of her generation. In 1868 she contracted a "fictitious marriage" with Vladimir Kovalevsky, a young palaeontology student, book publisher and radical, who was the first to translate and publish the works of Charles Darwin in Russia. They moved from Russia to Germany in 1869, after a brief stay in Vienna, in order to pursue advanced studies.Cooke, Roger. (1984) The Mathematics of Sonya Kovalevskaya, New York: Springer-Verlag.
Student years
In April 1869, following Sofia's and Vladimir's brief stay in Vienna, where she attended lectures in physics at the university, they moved to Heidelberg. Through great efforts, she obtained permission to audit classes with the professors' approval at the University of Heidelberg. There she attended courses in physics and mathematics under such teachers as Hermann von Helmholtz, Gustav Kirchhoff and Robert Bunsen. Vladimir, meanwhile, went on to the University of Jena to pursue a doctorate in palaeontology.
In October 1869, shortly after attending courses in Heidelberg, she visited London with Vladimir, who spent time with his colleagues Thomas Huxley and Charles Darwin, while she was invited to attend George Eliot's Sunday salons. There, at age nineteen, she met Herbert Spencer and was led into a debate, at Eliot's instigation, on "woman's capacity for abstract thought". Although there is no record of the details of their conversation, she had just completed a lecture course in Heidelberg on mechanics, and she may just possibly have made mention of the Euler equations governing the motion of a rigid body (see following section). Eliot was writing Middlemarch at the time, in which one finds the remarkable sentence: "In short, woman was a problem which, since Mr. Brooke's mind felt blank before it, could hardly be less complicated than the revolutions of an irregular solid."Eliot, George (Mary Ann Evans, 1871–1872 ), Middlemarch, Chapter IV, last sentence. This was well before Kovalevskaya's notable contribution of the "Kovalevskaya top" to the brief list of known examples of integrable rigid body motion (see following section).
In October 1870, Kovalevskaya moved to Berlin, where she began to take private lessons with Karl Weierstrass, since the university would not allow her even to audit classes. He was very impressed with her mathematical skills, and over the subsequent three years taught her the same material that comprised his lectures at the university. While studying under Weierstrass, Kovalevskaya lived with her friend Julia Lermontova, who became the first Russian woman to earn a doctorate in chemistry. Kovalevskaya referred to Vladimir as a brother and their marriage had not been consummated.
In 1871 Kovalevskaya briefly travelled to Paris together with Vladimir in order to help in the Paris Commune, where Kovalevskaya attended the injured and her sister Anyuta was active in the Commune. With the fall of the Commune, however, both Anyuta and her common law husband Victor Jaclard, who was leader of the Montmartre contingent of the National Guard and a prominent Blanquiste, were arrested. Although Anyuta managed to escape to London, Jaclard was sentenced to execution. However, with the assistance of Sofia's and Anyuta's father General Krukovsky, who had come urgently to Paris to help Anyuta and who wrote to Adolphe Thiers asking for clemency, Jaclard was saved.
Kovalevskaya returned to Berlin and continued her studies with Weierstrass for three more years. In 1874 she presented three papers—on partial differential equations, on the dynamics of Saturn's rings, and on elliptic integrals—to the University of Göttingen as her doctoral dissertation. With the support of Weierstrass, this earned her a doctorate in mathematics summa cum laude, after Weierstrass succeeded in having her exempted from the usual oral examinations.
Kovalevskaya was the first woman to have been awarded a doctorate (in the modern sense of the word) in mathematics, which occurred in 1874. Her paper on partial differential equations contains what is now commonly known as the Cauchy–Kovalevskaya theorem, which proves the existence and analyticity of local solutions to such equations under suitably defined initial/boundary conditions.
Last years in Germany and Sweden
In 1874, Kovalevskaya and her husband Vladimir returned to Russia, but Vladimir failed to secure a professorship because of his radical beliefs (Kovalevskaya never would have been considered for such a position because of her gender.) During this time they tried a variety of schemes to support themselves, including real estate development and involvement with an oil company. But in the late 1870s they faced serious financial problems, leading to bankruptcy.
In 1875, for some unknown reason, perhaps the death of her father, Sofia and Vladimir decided to spend several years together as an actual married couple. Three years later their daughter, Sofia (called "Fufa"), was born. After almost two years devoted to raising her daughter, Kovalevskaya put Fufa under the care of relatives and friends in Russia, resumed her work in mathematics, and left Vladimir for what would be the last time. Vladimir, who had always suffered severe mood swings, became more unstable. In 1883, faced with worsening mood swings and the possibility of being prosecuted for his role in a stock swindle, Vladimir died by suicide.
In 1881, Kovalevskaya was elected as a member of the Moscow Mathematical Society (MMS).
In 1883, with the help of the Swedish mathematician Gösta Mittag-Leffler, whom she had known as a fellow student of Weierstrass, Kovalevskaya was able to secure a position as a privat-docent at Stockholm University in Sweden. Kovalevskaya met Mittag-Leffler's sister, the actress, novelist, and playwright Anne Charlotte Edgren-Leffler. Until Kovalevskaya's death the two women shared a close friendship.McFadden, Margaret. (1999) Golden Cables of Sympathy: The Transatlantic Sources of Nineteenth-Century Feminism. University Press of Kentucky.
In 1884 Kovalevskaya was appointed to a five-year position as Extraordinary Professor (assistant professor in modern terminology) and became an editor of the journal Acta Mathematica. In 1888 she won the Prix Bordin of the French Academy of Science, for her work "Mémoire sur un cas particulier du problème de la rotation d'un corps pesant autour d'un point fixe, où l'intégration s'effectue à l'aide des fonctions ultraelliptiques du temps".Kovalevskaja, Sofya. (1894) Mémoire sur un cas particulier du problème de la rotation d'un corps pesant autour d'un point fixe où l'intégration s'effectue à l'aide de fonctions ultraelliptiques du temps, (In French). IMprimerie nationale. Her submission featured her celebrated discovery of what is now known as the "Kovalevskaya top", which was subsequently shown to be the only other case of rigid body motion that is "completely integrable" other than the tops of Euler and Lagrange.