Sofia Kovalevskaya
Encyclopedia
Sofia Vasilyevna Kovalevskaya ( – ), was the first major Russia
n female mathematician
, responsible for important original contributions to analysis, differential equations and mechanics, and the first woman appointed to a full professorship in Northern Europe.She was also one of the first females to work for a scientific journal as an editor.
There are some alternative transliterations
of her name. She herself used Sophie Kowalevski (or occasionally Kowalevsky), for her academic publications. After moving to Sweden, she called herself Sonya.
Korvin-Krukovskaya), was born in Moscow, the second of three children. Her father, Vasily Vasilyevich Korvin-Krukovsky, was Lieutenant-General of Artillery who served in the Imperial Russian Army
. Her mother, Yelizaveta Fedorovna Schubert, was a scholarly woman of German
ancestry and Sofia's grandmother was Romani. When she was 11 years old, the wall paper in her room had differential and integral analysis, which was her early preparation for calculus.
They nurtured her interest in mathematics and hired a tutor, (A. N. Strannoliubskii, a well-known advocate of higher education for women) who taught her calculus. During that same period, the son of the local priest introduced her to nihilism
.
Despite her obvious talent for mathematics, she could not complete her education in Russia. At that time, women there were not allowed to attend universities. In order to study abroad, she needed written permission from her father (or husband). Accordingly, she contracted a "fictitious marriage" with Vladimir Kovalevsky, then a young paleontology student who would later become famous for his collaboration with Charles Darwin
. They emigrated from Russia in 1867.
Shortly after beginning her studies there, 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". This was well before she made her notable contribution of the "Kovalevsky top" to the brief list of known examples of integrable rigid body motion (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."
After two years of mathematical studies at Heidelberg under such teachers as Hermann von Helmholtz
, Gustav Kirchhoff
and Robert Bunsen
, she moved to Berlin, where she had to take private lessons from Karl Weierstrass
, as the university would not even allow her to audit classes.
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, bypassing the usual required lectures and examinations.
She thereby became the first woman in Europe to hold that degree. Her paper on partial differential equations contains what is now commonly known as the Cauchy-Kovalevski theorem, which gives conditions for the existence of solutions to a certain class of those equations.
The Kovalevskys returned to Russia, but failed to secure professorships because of their radical political beliefs. Discouraged, they went back to Germany. Vladimir, who had always suffered severe mood swings, became more unstable so they spent most of their time apart. Then, for some unknown reason, they decided to spend several years together as an actual married couple. During this time their daughter, Sofia (called “Fufa”), was born. After a year devoted to raising her daughter, Kovalevskaya put Fufa under the care of her older sister, resumed her work in mathematics and left Vladimir for what would be the last time. In 1883, faced with worsening mood swings and the possibility of being prosecuted for his role in a stock swindle, Vladimir committed suicide.
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.
The following year (1884) she was appointed to a five year position as "Professor Extraordinarius" (Professor without Chair) and became the editor of Acta Mathematica
. In 1888 she won the Prix Bordin of the French Academy of Science, for her work on the question: "Mémoire sur un cas particulier du problème de le 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 included the celebrated discovery of what is now known as the "Kovalevsky top
", which was subsequently shown (by Liouville
) to be the only other case of rigid body
motion, beside the tops of Euler
and Lagrange
, that is "completely integrable".
In 1889 she was appointed Professor Ordinarius (Professorial Chair holder) at Stockholm University, the first woman to hold such a position at a northern European university. After much lobbying on her behalf (and a change in the Academy's rules) she was granted a Chair in the Russian Academy of Sciences
, but was never offered a professorship in Russia.
Kovalevskaya wrote several non-mathematical works as well, including a memoir, A Russian Childhood, plays (in collaboration with Duchess Anne Charlotte Edgren-Leffler) and a partly autobiographical novel
, Nihilist Girl (1890).
She died of influenza in 1891 at age forty-one, after returning from a pleasure trip to Genoa. She is buried in Solna
, Sweden, at Norra begravningsplatsen
(AWM), funding workshops across the United States which encourage girls to explore mathematics.
The Sonia Kovalevsky Lecture is sponsored annually by the AWM, and is intended to highlight significant contributions of women in the fields of applied or computational mathematics. Past honorees have included Irene Fonseca (2006), Ingrid Daubechies
(2005), Joyce R. McLaughlin (2004) and Linda R. Petzold (2003).
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.
Russia
Russia or , officially known as both Russia and the Russian Federation , is a country in northern Eurasia. It is a federal semi-presidential republic, comprising 83 federal subjects...
n female mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, responsible for important original contributions to analysis, differential equations and mechanics, and the first woman appointed to a full professorship in Northern Europe.She was also one of the first females to work for a scientific journal as an editor.
There are some alternative transliterations
Romanization of Russian
Romanization of the Russian alphabet is the process of transliterating the Russian language from the Cyrillic alphabet into the Latin alphabet...
of her name. She herself used Sophie Kowalevski (or occasionally Kowalevsky), for her academic publications. After moving to Sweden, she called herself Sonya.
Early years
Sofia Kovalevskaya (néeNEE
NEE is a political protest group whose goal was to provide an alternative for voters who are unhappy with all political parties at hand in Belgium, where voting is compulsory.The NEE party was founded in 2005 in Antwerp...
Korvin-Krukovskaya), was born in Moscow, the second of three children. Her father, Vasily Vasilyevich Korvin-Krukovsky, was Lieutenant-General of Artillery who served in the Imperial Russian Army
Imperial Russian Army
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 around 938,731 regular soldiers and 245,850 irregulars . Until the time of military reform of Dmitry Milyutin in...
. Her mother, Yelizaveta Fedorovna Schubert, was a scholarly woman of German
Germans
The Germans are a Germanic ethnic group native to Central Europe. The English term Germans has referred to the German-speaking population of the Holy Roman Empire since the Late Middle Ages....
ancestry and Sofia's grandmother was Romani. When she was 11 years old, the wall paper in her room had differential and integral analysis, which was her early preparation for calculus.
They nurtured her interest in mathematics and hired a tutor, (A. N. Strannoliubskii, a well-known advocate of higher education for women) who taught her calculus. During that same period, the son of the local priest introduced her to nihilism
Nihilism
Nihilism is the philosophical doctrine suggesting the negation of one or more putatively meaningful aspects of life. Most commonly, nihilism is presented in the form of existential nihilism which argues that life is without objective meaning, purpose, or intrinsic value...
.
Despite her obvious talent for mathematics, she could not complete her education in Russia. At that time, women there were not allowed to attend universities. In order to study abroad, she needed written permission from her father (or husband). Accordingly, she contracted a "fictitious marriage" with Vladimir Kovalevsky, then a young paleontology student who would later become famous for his collaboration with Charles Darwin
Charles Darwin
Charles Robert Darwin FRS was an English naturalist. He established that all species of life have descended over time from common ancestry, and proposed the scientific theory that this branching pattern of evolution resulted from a process that he called natural selection.He published his theory...
. They emigrated from Russia in 1867.
Student Years
In 1869, Kovalevskaya began attending the University of Heidelberg, Germany, which allowed her to audit classes as long as the professors involved gave their approval.Shortly after beginning her studies there, she visited London with Vladimir, who spent time with his colleagues Thomas Huxley
Thomas Huxley
Thomas Henry Huxley PC FRS was an English biologist, known as "Darwin's Bulldog" for his advocacy of Charles Darwin's theory of evolution....
and Charles Darwin
Charles Darwin
Charles Robert Darwin FRS was an English naturalist. He established that all species of life have descended over time from common ancestry, and proposed the scientific theory that this branching pattern of evolution resulted from a process that he called natural selection.He published his theory...
, while she was invited to attend George Eliot
George Eliot
Mary Anne Evans , better known by her pen name George Eliot, was an English novelist, journalist and translator, and one of the leading writers of the Victorian era...
's Sunday salons. There, at age nineteen, she met Herbert Spencer
Herbert Spencer
Herbert Spencer was an English philosopher, biologist, sociologist, and prominent classical liberal political theorist of the Victorian era....
and was led into a debate, at Eliot's instigation, on "woman's capacity for abstract thought". This was well before she made her notable contribution of the "Kovalevsky top" to the brief list of known examples of integrable rigid body motion (see following section). George Eliot was writing Middlemarch
Middlemarch
Middlemarch: A Study of Provincial Life is a novel by George Eliot, the pen name of Mary Anne Evans, later Marian Evans. It is her seventh novel, begun in 1869 and then put aside during the final illness of Thornton Lewes, the son of her companion George Henry Lewes...
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."
After two years of mathematical studies at Heidelberg under such teachers as Hermann von Helmholtz
Hermann von Helmholtz
Hermann Ludwig Ferdinand von Helmholtz was a German physician and physicist who made significant contributions to several widely varied areas of modern science...
, Gustav Kirchhoff
Gustav Kirchhoff
Gustav Robert Kirchhoff was a German physicist who contributed to the fundamental understanding of electrical circuits, spectroscopy, and the emission of black-body radiation by heated objects...
and Robert Bunsen
Robert Bunsen
Robert Wilhelm Eberhard Bunsen was a German chemist. He investigated emission spectra of heated elements, and discovered caesium and rubidium with Gustav Kirchhoff. Bunsen developed several gas-analytical methods, was a pioneer in photochemistry, and did early work in the field of organoarsenic...
, she moved to Berlin, where she had to take private lessons from Karl Weierstrass
Karl Weierstrass
Karl Theodor Wilhelm Weierstrass was a German mathematician who is often cited as the "father of modern analysis".- Biography :Weierstrass was born in Ostenfelde, part of Ennigerloh, Province of Westphalia....
, as the university would not even allow her to audit classes.
In 1874 she presented three papers—on partial differential equations, on the dynamics of Saturn
Saturn
Saturn is the sixth planet from the Sun and the second largest planet in the Solar System, after Jupiter. Saturn is named after the Roman god Saturn, equated to the Greek Cronus , the Babylonian Ninurta and the Hindu Shani. Saturn's astronomical symbol represents the Roman god's sickle.Saturn,...
's rings
Rings of Saturn
The rings of Saturn are the most extensive planetary ring system of any planet in the Solar System. They consist of countless small particles, ranging in size from micrometres to metres, that form clumps that in turn orbit about Saturn...
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, bypassing the usual required lectures and examinations.
She thereby became the first woman in Europe to hold that degree. Her paper on partial differential equations contains what is now commonly known as the Cauchy-Kovalevski theorem, which gives conditions for the existence of solutions to a certain class of those equations.
Last Years in Germany and Sweden
In the early 1880’s, Sonya and her husband Vladimir developed financial problems. Sonya wanted to be a lecturer at the university; however, she was not allowed to because she was a woman, even though she had the same amount of knowledge in mathematics as men. Sonya had even volunteered to provide free lectures and she was still denied the right. Soon after, Vladimir started business management and Sonya became his assistant. They built houses as well as fountains to become financially stable again for a short period of time. In 1879, the price for mortgages became higher than the amount of money they made. They lost all their money again and became bankrupt. Shortly after, Vladimir got a job offer and Sonya helped neighbours to electrify street lights. Vladimir and Sonya quickly established themselves again financially.The Kovalevskys returned to Russia, but failed to secure professorships because of their radical political beliefs. Discouraged, they went back to Germany. Vladimir, who had always suffered severe mood swings, became more unstable so they spent most of their time apart. Then, for some unknown reason, they decided to spend several years together as an actual married couple. During this time their daughter, Sofia (called “Fufa”), was born. After a year devoted to raising her daughter, Kovalevskaya put Fufa under the care of her older sister, resumed her work in mathematics and left Vladimir for what would be the last time. In 1883, faced with worsening mood swings and the possibility of being prosecuted for his role in a stock swindle, Vladimir committed suicide.
That year, with the help of the mathematician Gösta Mittag-Leffler, whom she had known as a fellow student of Weierstrass'
Karl Weierstrass
Karl Theodor Wilhelm Weierstrass was a German mathematician who is often cited as the "father of modern analysis".- Biography :Weierstrass was born in Ostenfelde, part of Ennigerloh, Province of Westphalia....
, Kovalevskaya was able to secure a position as a privat-docent at Stockholm University
Stockholm University
Stockholm University is a state university in Stockholm, Sweden. It has over 28,000 students at four faculties, making it one of the largest universities in Scandinavia. The institution is also frequently regarded as one of the top 100 universities in the world...
in Sweden.
The following year (1884) she was appointed to a five year position as "Professor Extraordinarius" (Professor without Chair) and became the editor of Acta Mathematica
Acta Mathematica
Acta Mathematica is a journal publishing original research papers in all fields of mathematics. The journal was founded by Gösta Mittag-Leffler in 1882 and is published by Institut Mittag-Leffler, a research institute for mathematics belonging to the Royal Swedish Academy of Sciences...
. In 1888 she won the Prix Bordin of the French Academy of Science, for her work on the question: "Mémoire sur un cas particulier du problème de le 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 included the celebrated discovery of what is now known as the "Kovalevsky top
Kovalevskaya Top
The Kovalevskaya Top is one of a brief list of known examples of integrable rigid body motion . It was discovered by Sofia Kovalevskaya in 1888 and presented in her paper 'Sur Le Probleme De La Rotation D'Un Corps Solide AutourD'Un Point Fixe' ....
", which was subsequently shown (by Liouville
Joseph Liouville
- Life and work :Liouville graduated from the École Polytechnique in 1827. After some years as an assistant at various institutions including the Ecole Centrale Paris, he was appointed as professor at the École Polytechnique in 1838...
) to be the only other case of rigid body
Rigid body
In physics, a rigid body is an idealization of a solid body of finite size in which deformation is neglected. In other words, the distance between any two given points of a rigid body remains constant in time regardless of external forces exerted on it...
motion, beside the tops of Euler
Leonhard Euler
Leonhard Euler was a pioneering Swiss mathematician and physicist. He made important discoveries in fields as diverse as infinitesimal calculus and graph theory. He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion...
and Lagrange
Joseph Louis Lagrange
Joseph-Louis Lagrange , born Giuseppe Lodovico Lagrangia, was a mathematician and astronomer, who was born in Turin, Piedmont, lived part of his life in Prussia and part in France, making significant contributions to all fields of analysis, to number theory, and to classical and celestial mechanics...
, that is "completely integrable".
In 1889 she was appointed Professor Ordinarius (Professorial Chair holder) at Stockholm University, the first woman to hold such a position at a northern European university. After much lobbying on her behalf (and a change in the Academy's rules) she was granted a Chair in the Russian Academy of Sciences
Russian Academy of Sciences
The Russian Academy of Sciences consists of the national academy of Russia and a network of scientific research institutes from across the Russian Federation as well as auxiliary scientific and social units like libraries, publishers and hospitals....
, but was never offered a professorship in Russia.
Kovalevskaya wrote several non-mathematical works as well, including a memoir, A Russian Childhood, plays (in collaboration with Duchess Anne Charlotte Edgren-Leffler) and a partly autobiographical novel
Biographical novel
The biographical novel is a genre of novel which provides a fictional and usually entertaining account of a person's life. This kind of novel concentrates on the experiences a person had during his lifetime, the people he met and the incidents which occurred are detailed and sometimes...
, Nihilist Girl (1890).
She died of influenza in 1891 at age forty-one, after returning from a pleasure trip to Genoa. She is buried in Solna
Solna Municipality
Solna Municipality is a municipality in Stockholm County in east central Sweden, located just north of the capital Stockholm. Its seat is located in the 'city' of Solna....
, Sweden, at Norra begravningsplatsen
Norra begravningsplatsen
Norra begravningsplatsen, literally "The Northern Cemetery" in Swedish, is a major cemetery of Metropolitan Stockholm. The cemetery is located in the municipality of Solna.Inaugurated on June 9, 1827, it is the burial site for a number of Swedish notables....
Tributes
Sonia Kovalevsky High School Mathematics Day is a grant-making program of the Association for Women in MathematicsAssociation for Women in Mathematics
The Association for Women in Mathematics is a professional society whose mission is to encourage women and girls to study and to have active careers in the mathematical sciences. Equal opportunity and the equal treatment of women and girls in the mathematical sciences are promoted. The AWM was...
(AWM), funding workshops across the United States which encourage girls to explore mathematics.
The Sonia Kovalevsky Lecture is sponsored annually by the AWM, and is intended to highlight significant contributions of women in the fields of applied or computational mathematics. Past honorees have included Irene Fonseca (2006), Ingrid Daubechies
Ingrid Daubechies
Ingrid Daubechies is a Belgian physicist and mathematician. She was between 2004 and 2011 the William R. Kenan Jr. Professor in the mathematics and applied mathematics departments at Princeton University. In January 2011 she moved to Duke University as a Professor in mathematics. She is the first...
(2005), Joyce R. McLaughlin (2004) and Linda R. Petzold (2003).
The lunar crater Kovalevskaya
Kovalevskaya (crater)
Kovalevskaya is a prominent lunar impact crater that is located on the Moon's far side. It lies to the southwest of the larger walled plain Landau. To the south of Kovalevskaya are the craters Poynting and Fersman....
is named in her honor.
The Alexander Von Humboldt Foundation of Germany bestows a bi-annual Sofia Kovalevskaya Award
Sofia Kovalevskaya Award
The Alexander Von Humboldt Foundation of Germany bestows the Sofia Kovalevskaya Award every two years. Sofia Kovalevskaya was the first major Russian female mathematician, who made important contributions to mathematical analysis, differential equations and mechanics, and the first woman...
to promising young researchers.
In Film
Sofia Kovalevskaya has been the subject of three film and TV biographies.- Sofya Kovalevskaya (1956) directed by Iosef Shapiro, starring Yelena Yunger, Lev Kosolov and Tatyana Sezenyevskaya.
- Berget På Månens Baksida ("A Hill on the Dark Side of the Moon") (1983) directed by Lennart HjulströmLennart HjulströmLennart Hjalmar Hjulström is a Swedish actor and director. He is married to Gunilla Nyroos and father to Niklas and Carin Hjulström...
, starring Gunilla Nyroos as Sofja Kovalewsky and Bibi AnderssonBibi AnderssonBibi Andersson is a Swedish actress.-Early life:Bibi Andersson was born as Berit Elisabeth Andersson in Kungsholmen, Stockholm, the daughter of Karin , a social worker, and Josef Andersson, a businessman...
as Anne Charlotte Edgren-Leffler, Duchess of Cajanello, and sister to Gösta Mittag-Leffler.
- Sofya Kovalevskaya (1985 TV) directed by Ayan Shakhmaliyeva, starring Yelena Safonova as Sofia.
In fiction
- "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 DohertyTom DohertyTom Doherty is an American publisher, and the founder of Tor Books. After working as a book salesman in the 1950s and 1960s, Doherty became publisher of Tempo Books in 1972; in 1975, he became, in addition, publisher of another company also owned by Grosset & Dunlap, the science fiction imprint...
Associates, LLC, is an historically accurate portrayal of her early married years and quest for an education. It is based in part on 88 of Sofia's letters, which the author translated from Russian to English.
- Against the DayAgainst the DayAgainst the Day is a novel by Thomas Pynchon. The narrative takes place between the 1893 Chicago World's Fair and the time immediately following World War I and features more than a hundred characters spread across the United States, Europe, Mexico, Central Asia, and "one or two places not strictly...
, a 2006 novel by Thomas PynchonThomas PynchonThomas Ruggles Pynchon, Jr. is an American novelist. For his most praised novel, Gravity's Rainbow, Pynchon received the National Book Award, and is regularly cited as a contender for the Nobel Prize in Literature...
was speculated before release to be based on the life of Sofia, but in the finished novel she appears as a minor character.
- "Too Much Happiness" (2009), short story by Alice MunroAlice MunroAlice Ann Munro is a Canadian short-story writer, the winner of the 2009 Man Booker International Prize for her lifetime body of work, a three-time winner of Canada's Governor General's Award for fiction, and a perennial contender for the Nobel Prize...
, published in the August 2009 issue of Harper's MagazineHarper's MagazineHarper's Magazine is a monthly magazine of literature, politics, culture, finance, and the arts, with a generally left-wing perspective. It is the second-oldest continuously published monthly magazine in the U.S. . The current editor is Ellen Rosenbush, who replaced Roger Hodge in January 2010...
features Sofia as a main character. It was later published in a collection of the same nameToo Much HappinessToo Much Happiness is a short story collection by Canadian writer Alice Munro, published on August 25, 2009 by McClelland and Stewart's Douglas Gibson Books imprint....
.
Novel
- Nihilist Girl, translated by Natasha Kolchevska with Mary Zirin ; introduction by Natasha Kolchevska. Modern Language Association of America (2001) ISBN 0-87352-790-9
See also
- Ann Hibner Koblitz: A Convergence of Lives: Sofia Kovalevskaia -- Scientist, Writer, Revolutionary (Rutgers University Press, 1983)
- A. H. Koblitz, Sofia Vasilevna Kovalevskaia in
- Roger Cooke, The Mathematics of Sonya Kovalevskaya (Springer-Verlag, 1984)
External links
- "Sofia Kovalevskaya", Biographies of Women Mathematicians, Agnes Scott CollegeAgnes Scott CollegeAgnes Scott College is a private undergraduate college in the United States. Agnes Scott's campus lies in downtown Decatur, Georgia, nestled inside the perimeter of the bustling metro-Atlanta area....
- Women's History - Sofia Kovalevskaya
- Brief biography of Sofia Kovalevskaya by Yuriy Belits. University of Colorado at Denver, March 17, 2005.
- Biography (in Russian)
- Association for Women in Mathematics