Sofia Kovalevskaya

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Sofia Kovalevskaya
Sofja Wassiljewna Kowalewskaja 1.jpg
Sofia Kovalevskaya in 1880
Born(1850-01-15)15 January 1850
Died10 February 1891(1891-02-10) (aged 41)
Stockholm, Sweden
Alma mater University of Göttingen (PhD; 1874)
Known for Cauchy–Kowalevski theorem
Scientific career
FieldsMathematics, Mechanics
Doctoral advisor Karl Weierstrass

Sofia Vasilyevna Kovalevskaya (Russian: Софья Васильевна Ковалевская), born Sofia Vasilyevna Korvin-Krukovskaya (15 January [ O.S. 3 January] 1850 – 10 February 1891), was a Russian mathematician who made noteworthy contributions to analysis, partial differential equations and mechanics. She was a pioneer for women in mathematics around the world – the first woman to obtain a doctorate (in the modern sense) in mathematics, the first woman appointed to a full professorship in Northern Europe and one of the first women to work for a scientific journal as an editor. [1] According to historian of science Ann Hibner Koblitz, Kovalevskaia was "the greatest known woman scientist before the twentieth century". [2] :255

Old Style and New Style dates 16th-century changes in calendar conventions

Old Style (O.S.) and New Style (N.S.) are terms sometimes used with dates to indicate that the calendar convention used at the time described is different from that in use at the time the document was being written. There were two calendar changes in Great Britain and its colonies, which may sometimes complicate matters: the first was to change the start of the year from Lady Day to 1 January; the second was to discard the Julian calendar in favour of the Gregorian calendar. Closely related is the custom of dual dating, where writers gave two consecutive years to reflect differences in the starting date of the year, or to include both the Julian and Gregorian dates.

Mathematical analysis Branch of mathematics

Mathematical analysis is the branch of mathematics dealing with limits and related theories, such as differentiation, integration, measure, infinite series, and analytic functions.

Partial differential equation differential equation that contains unknown multivariable functions and their partial derivatives

In mathematics, a partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives. PDEs are used to formulate problems involving functions of several variables, and are either solved by hand, or used to create a computer model. A special case is ordinary differential equations (ODEs), which deal with functions of a single variable and their derivatives.


Historian of mathematics Roger Cooke writes:

... the more I reflect on her life and consider the magnitude of her achievements, set against the weight of the obstacles she had to overcome, the more I admire her. For me she has taken on a heroic stature achieved by very few other people in history. To venture, as she did, into academia, a world almost no woman had yet explored, and to be consequently the object of curious scrutiny, while a doubting society looked on, half-expecting her to fail, took tremendous courage and determination. To achieve, as she did, at least two major results of lasting value to scholarship, is evidence of a considerable talent, developed through iron discipline. [3] :1

Her sister was the socialist Anne Jaclard.

There are several alternative transliterations of her name. She herself used Sophie Kowalevski (or occasionally Kowalevsky) in her academic publications.

Romanization of Russian Romanization of the Russian alphabet

Romanization of Russian is the process of transliterating the Russian language from the Cyrillic script into the Latin script.

Background and early education

Sofia Kovalevskaya ( née Korvin-Krukovskaya), was born in Moscow, the second of three children. Her father, Lieutenant General Vasily Vasilyevich Korvin-Krukovsky, served in the Imperial Russian Army as head of the Moscow Artillery before retiring to Palibino, his family estate in Vitebsk Region in 1858, when Sofia was eight years old. He was a member of the minor nobility, of mixed (Bela)Russian–Polish descent (Polish on his father's side), with possible partial ancestry from the royal Korvin 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. [4] )

Imperial Russian Army land armed force of the Russian Empire

The Imperial Russian Army was the land armed force of the Russian Empire, active from around 1721 to the Russian Revolution of 1917. In the early 1850s, the Russian army consisted of more than 900,000 regular soldiers and nearly 250,000 irregulars.

Vitebsk Region Place in Vitsebsk

Vitebsk Region, Vitsebsk Voblast, or Vitebsk Oblast is a region (voblast) of Belarus with its administrative center being Vitebsk (Vitsebsk). It is located near the border with Russia.

Poles West Slavic nation native to Poland

The Poles, commonly referred to as the Polish people, are a nation and West Slavic ethnic group native to Poland in Central Europe who share a common ancestry, culture, history, and are native speakers of the Polish language. The population of self-declared Poles in Poland is estimated at 37,394,000 out of an overall population of 38,538,000, of whom 36,522,000 declared Polish alone.

Her mother, Yelizaveta Fedorovna Shubert (Schubert), 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 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, Sofia's maternal grandfather, was General Theodor Friedrich von Schubert (Shubert) [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.

Friedrich Theodor von Schubert was a German astronomer and geographer. Born in Helmstedt, his father, Johann Ernst Schubert, was a professor of theology and abbot of Michaelstein Abbey. Theodor likewise studied theology, but didn't like it. He traveled abroad, first to Sweden in 1779. He then went to Bartelshagen, where he became the tutor of the children of Major von Cronhelm. Since the major was fond of mathematics and astronomy, Theodor had to study these himself to be able to teach those subjects. He then married the daughter of the major, Luise Friederike von Cronhelm. Afterwards, he traveled to Tallinn in Estonia, again as a house teacher. He moved on to Haapsalu, teaching mathematics to young noblemen as a preparation for a life as an officer. In 1785 he became an assistant of the Russian Academy of Sciences as a geographer, and by June 1789 he was a full member. In 1803, he became head of the astronomical observatory of the Academy. In 1805, he was a member of the failed Russian expedition to China, together with his son. He was elected a Foreign Honorary Member of the American Academy of Arts and Sciences in 1812.

Friedrich von Schubert Russian general

Theodor Friedrich von Schubert (1789–1865) was a Baltic German general and scientist. Born in Saint Petersburg as the son of astronomer Theodor von Schubert. When he was sixteen years old, he accompanied his father on the Russian expedition to China. He was married to Sophie Rall, and had four children. He became an infantry general in the Russian army, head of the military topographic service, and honorary member of the Russian Academy of Sciences. As an officer, he fought in the War of the Fourth Coalition in 1806, in the Finnish War in 1808 and in the Russo-Turkish War in 1810. by 1812, he was an upper quartermaster general, and at the battle of Leipzig in 1815, he became a colonel. Between 1815 and 1818, he stayed with the Russian occupation force in France, before returning to Russia as part of the general staff. He was interested in cartography. In 1845, he became an infantry general. He died in Stuttgart in 1865, after having spent his last years traveling.

Sofia'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 8 or 9 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 Ostrogradsky, left over from her father's student days. [5] She was tutored privately in elementary mathematics by Iosif Ignatevich Malevich.

Mikhail Ostrogradsky Russian mathematician

Mikhail Vasilyevich Ostrogradsky was a Russian mathematician, mechanician and physicist. Ostrogradsky was a student of Timofei Osipovsky and is considered to be a disciple of Leonhard Euler and one of the leading mathematicians of Imperial Russia.

The physicist Nikolai Nikanorovich Tyrtov noted her 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. [6] Tyrtov called her a "new Pascal" and suggested she be given a chance to pursue further studies under the tutelage of N. Strannoliubskii. [7] 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 "Movement of the 1860's", providing her with copies of radical journals of the time discussing nihilism. [8]

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):

After the famous writer Ivan Turgenev used the word nihilist to refer to Bazarov, the young hero of his 1862 novel Fathers and Children, a certain segment of the "new people" adopted that name as well, despite its negative connotations in most quarters.... For the nihilists, science appeared to be the most effective means of helping the mass of people to a better life. Science pushed back the barriers of religion and superstition, and "proved" through the theory of evolution that (peaceful) social revolutions were the way of nature. For the early nihilists, science was virtually synonymous with truth, progress and radicalism; thus, the pursuit of a scientific career was viewed in no way as a hindrance to social activism. In fact, it was seen as a positive boost to progressive forces, an active blow against backwardness. [9] :2–4

Despite Sofia's obvious talent for mathematics, she 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, Sofia needed written permission from her father (or husband). Accordingly, in 1868 she contracted a "fictitious marriage" with Vladimir Kovalevskij, a young paleontology 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. [10]

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. [2] :87–89 Vladimir, meanwhile, went on to the University of Jena to pursue a doctorate in paleontology.

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. [10] 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). George 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." [11] This was well before she made her notable contribution of the "Kovalevskaya top" to the brief list of known examples of integrable rigid body motion (see following section).

In October 1870, Sofia 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.

In 1871 she briefly traveled to Paris together with Vladimir in order to help in the Paris Commune, where Sofia attended the injured and her sister Anyuta was active in the Commune. [2] :104–106 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, they managed to save Victor Jaclard. [2] :107–108

Sofia 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. [10]

Kovalevskaya thereby became the first woman to have been awarded a doctorate at a European university. 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

Bust by Finnish sculptor Walter Runeberg Sofya Vasilyevna Kovalevskaya Bust.jpg
Bust by Finnish sculptor Walter Runeberg
Sofia Kovalevskaya's grave, Norra begravningsplatsen Sofia Kovalevskaya grave.jpg
Sofia Kovalevskaya's grave, Norra begravningsplatsen

In 1874, Sofia and her husband Vladimir returned to Russia, but Vladimir failed to secure a professorship because of his radical beliefs. (Sofia 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 developed financial problems, leading to bankruptcy. [12] [2]

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, 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 committed suicide. [10]

That year, with the help of the 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. [10] 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. [13]

In 1884 Kovalevskaya was appointed to a five-year position as Extraordinary Professor (assistant professor in modern terminology) and became an editor of 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". [10] [14] Her submission featured the 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. [15]

In 1889 Kovalevskaya was appointed Ordinary Professor (full professor) at Stockholm University, the first woman in Europe in modern times to hold such a position. [2] :218 After much lobbying on her behalf (and a change in the Academy's rules) she was made a Corresponding Member of the Russian Academy of Sciences, but she was never offered a professorship in Russia.

Kovalevskaya, who was involved in the vibrant, politically progressive and feminist currents of late nineteenth-century Russian nihilism, wrote several non-mathematical works as well, including a memoir, A Russian Childhood, two plays (in collaboration with Duchess Anne Charlotte Edgren-Leffler) and a partly autobiographical novel, Nihilist Girl (1890).

In 1889, Kovalevskaya fell in love with Maxim Kovalevsky, a distant relation of her deceased husband, [16] but insisted on not marrying him because she would not be able to settle down and live with him. [3] :18

Kovalevskaya died of influenza complicated by pneumonia in 1891 at age forty-one, after returning from a vacation in Nice with Maxim. [2] :231 She is buried in Solna, Sweden, at Norra begravningsplatsen.

Kovalevskaya's mathematical results, such as the Cauchy–Kowalevski theorem, and her pioneering role as a female mathematician in an almost exclusively male-dominated field, have made her the subject of several books, including a biography by Ann Hibner Koblitz, [2] a biography in Russian by Polubarinova-Kochina [17] (translated into English by M. Burov with the title Love and Mathematics: Sofya Kovalevskaya, Mir Publishers, 1985), and a book about her mathematics by R. Cooke. [10]


Commemorative coin, 2000. RR5110-0034R.gif
Commemorative coin, 2000.
Soviet Union postage stamp, 1951. Stamp of USSR 1635g.jpg
Soviet Union postage stamp, 1951.

Sonya Kovalevsky High School Mathematics Day is a grant-making program of the Association for Women in Mathematics (AWM), funding workshops across the United States which encourage girls to explore mathematics. While the AWM currently does not have grant money to support this program, multiple universities continue the program with their own funding [18] .

The Sonya Kovalevsky Lecture is sponsored annually by the AWM and the Society for Industrial and Applied Mathematics, and is intended to highlight significant contributions of women in the fields of applied or computational mathematics.

The Kovalevskaia Fund, founded in 1985 with the purpose of supporting women in science in developing countries, was named in her honor.

The lunar crater Kovalevskaya is named in her honor.

The Alexander Von Humboldt Foundation of Germany bestows a bi-annual Sofia Kovalevskaya Award to promising young researchers.

Saint Petersburg, Moscow, and Stockholm have streets named in honor of Sofia Kovalevskaya.

In film

Sofia Kovalevskaya has been the subject of three film and TV biographies.

In fiction

See also

Selected publications


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  1. "Sofya Vasilyevna Kovalevskaya". Encyclopædia Britannica Online Academic Edition. Encyclopædia Britannica. Retrieved 22 October 2011.
  2. 1 2 3 4 5 6 7 8 Koblitz, Ann Hibner (1993). A convergence of lives: Sofia Kovalevskaia: scientist, writer, revolutionary (Reprinted in hardcover. ed.). New Brunswick (New Jersey): Rutgers University Press. ISBN   9780813519630.
  3. 1 2 Roger L. Cooke, "The life of S. V. Kovalevskaya", in V. B. Kuznetsov, ed., The Kowalevski Property, American Mathematical Society, 2002, p. 1–19.
  4. Marie-Louise Dubreil-Jacotin. "Women mathematicians". JOC/EFR. Archived from the original on June 7, 2011. Retrieved June 3, 2012.
  5. "Best of Russia --- Famous Russians --- Scientists". TRISTARMEDIA | Web Design, Web Development, Multimedia, Creative Web Solutions. Archived from the original on 3 September 2011. Retrieved 21 October 2011.Cite uses deprecated parameter |deadurl= (help)
  6. F. V. Korvin-Krukovskii, "Sofia Vasilevna Korvin-Krukovskaia," Russkaia Starina, vol. 71, no. 9 (1891), p. 623-636.
  7. Rappaport, Karen D. "S. Kovalevsky: A Mathematical Lesson." The American Mathematical Monthly 88 (October 1981): 564-573.
  8. Sofya Kovalevskaya, A Russian Childhood, translated, edited, and introduced by Beatrice Stillman ; with an analysis of Kovalevskaya's Mathematics by P. Y. Kochina. Springer-Verlag, c1978 ISBN   0-387-90348-8
  9. Ann Hibner Koblitz, Science, Women and Revolution in Russia, Routledge, 2000.
  10. 1 2 3 4 5 6 7 Roger Cooke, The Mathematics of Sonya Kovalevskaya, Springer-Verlag, 1984.
  11. George Eliot (Mary Ann Evans), Middlemarch, Chapter IV, last sentence.
  12. Kochina, Pelageya (1985). Love and Mathematics: Sofia Kovalevskaya. Moscow: Mir Publisher.
  13. McFadden, Margaret. Golden Cables of Sympathy: The Transatlantic Sources of Nineteenth-Century Feminism. University Press of Kentucky, 1999.
  14. Sofʹja Vasilʹevna Kovalevskaja, 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 , IMprimerie nationale, 1894
  15. Cooke, Roger (1984). The Mathematics of Sonya Kovalevskaya. Springer. p. 159. ISBN   9781461297666.
  16. Bruno, Leonard C. (2003) [1999]. Math and mathematicians : the history of math discoveries around the world. Baker, Lawrence W. Detroit, Mich.: U X L. p. 251. ISBN   0787638145. OCLC   41497065.
  17. P. Ia. Polubarinova-Kochina, Sofia Vasilevna Kovalevskaia 1850-1891, Nauka, 1981.
  18. "Kovalevsky Days - AWM Association for Women in Mathematics". Retrieved 2018-08-21.
  19. 'Sofya Kovalevskaya' on IMDb
  20. 'Berget på månens baksida' on IMDb
  21. 'Sofya Kovalevskaya' on IMDb

Further reading

This article incorporates material from Sofia Kovalevskaya on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.