Sofia Kovalevskaya

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. )

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. Tyrtov called her a "new Pascal" and suggested she be given a chance to pursue further studies under the tutelage of . 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.

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. They moved from Russia to Germany in 1869, after a brief stay in Vienna, in order to pursue advanced studies.

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. 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." 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,

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 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". 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. thumb

In 1889, Kovalevskaya fell in love with Russian jurist Maxim Kovalevsky, a distant relation of her deceased husband, but insisted on not marrying him because she would not be able to settle down and live with him. (translated into English by M. Burov with the title Love and Mathematics: Sofya Kovalevskaya, Mir Publishers, 1985), a book titled Remembering Sofya Kovalevskaya by French mathematician Michèle Audin, and a book about her mathematics by Roger Cooke. The official was published by the Minor Planet Center on 1 June 1975 .

In 1985 Ann Hibner Koblitz and her husband Neal established the Kovalevskaia Fund; a non-profit organization whose purpose is to support and encourage women in developing countries in science, mathematics, engineering, and medicine. It was originally aimed at promoting women in the sciences in Vietnam; it grew out of Ann's work on the history of women and science, her and Neal's experience in the opposition to United States involvement in the Vietnam War, and their efforts to help promote science in Vietnam afterwards.

The Kovalevskaya Prize is a national scientific prize awarded by the Russian Academy of Sciences for outstanding achievements in mathematics, since 1997. The foundation encouraged applications from all areas of learning so long as the applicant had received a Ph.D. in the previous six years and could be categorized as "top flight" by their publications and experience as commensurate with age.

The AWM-SIAM Sonia Kovalevsky Lecture is an award and lecture series that "highlights the achievements of women in applied and computational mathematics." and lecture series in 2002 and first awarded it in 2003. The lecture is normally given each year at the SIAM Annual Meeting.

On 30 June 2021, a satellite named after her (also called ÑuSat 22) was launched.

On January 15, 2025, a postage stamp honoring her 175th birthday was put into circulation in Russia. The stamp features a portrait of her, a Kovalevskaya top, and “formulae illustrating the study of the rotation of a heavy asymmetric body around a fixed point.”

The lunar crater Kovalevskaya is named in her honor.

A school in Vilnius, Lithuania, is named after her, called Sofija Kovalevskaja Gymnasium. There was another school in Vilnius named after her, called Sofija Kovalevskaja Progymnasium, but in 2024 its name was changed to Vilnius "Sostinės" gymnasium.

Sofya 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.

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

Sofya Kovalevskaya (1956) directed by Iosef Shapiro, starring Yelena Yunger, Lev Kolesov and Tatyana Sezenyevskaya. Berget på månens baksida ("A Hill on the Dark Side of the Moon") (1983) directed by Lennart Hjulström, starring Gunilla Nyroos as Sofja Kovalewsky and Bibi Andersson as Anne Charlotte Edgren-Leffler, Duchess of Cajanello, and sister to Gösta Mittag-Leffler. Sofya Kovalevskaya (1985 TV) directed by Azerbaijani director Ayan Shakhmaliyeva, starring Yelena Safonova as Sofia.

In literature Little Sparrow: A Portrait of Sophia Kovalevsky (1983), Don H. Kennedy, Ohio University Press, Athens, Ohio Beyond the Limit: The Dream of Sofya Kovalevskaya (2002), , a biographical novel by mathematician and educator Joan Spicci, published by Tom Doherty Associates Against the Day, a 2006 novel by Thomas Pynchon, was speculated before release to be based on the life of Kovalevskaya, but in the finished novel she appears as a minor character. "Too Much Happiness" (2009), a short story by Alice Munro, published in the August 2009 issue of Harper's Magazine, features Kovalevskaya as a main character. It was later published in a collection of the same name.

Poet Jessy Randall's 2022 collection Mathematics for Ladies includes a poem honoring Kovalevskaya.