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Sofia Vasilyevna Kovalevskaya (15 January 1850 – 10 February 1891) was the first major Russian 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 women to work for a scientific journal as an editor. Sophia's lover in later life was Anne Charlotte Leffler-Edgren (1849-1892), the duchess of Cajanello. The two women wrote a number of books and plays together, including A Struggle for Happiness. Leffler-Edgren wrote a short biography of Kovalevsky as an introduction to the mathematician's autobiography.

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. (Picture: Anne Charlotte Leffler-Edgren)

Sofia Kovalevskaya (née 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.

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 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." Kovalevskaya participated in social movements and shared ideas of utopian socialism. In 1871 she traveled to Paris together with her husband in order to attend to the injured from the Paris Commune. Kovalevskaya helped save Victor Jaclard, who was the husband of her sister Ann (Anne Jaclard).

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.

In the early 1880s, Sofia and her husband Vladimir developed financial problems. Sofia 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. Sofia had even volunteered to provide free lectures and she was still denied the right. Soon after, Vladimir started business management and Sofia 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 Sofia helped neighbours to electrify street lights. Vladimir and Sofia 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', 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.

Sofia Kovalevskaya has been the subject of three film and TV biographies. Berget På Månens Baksida ("A Hill on the Dark Side of the Moon") (1983) directed by Lennart Hjulström, stars Gunilla Nyroos as Sofja Kovalewsky and Bibi Andersson as Anne Charlotte Edgren-Leffler, Duchess of Cajanello, and sister to Gösta Mittag-Leffler.

Source: http://en.wikipedia.org/wiki/Sofia_Kovalevskaya

Further Readings:

Beyond the Limit: The Dream of Sofya Kovalevskaya by Joan Spicci
Hardcover: 496 pages
Publisher: Forge Books; 1st edition (August 24, 2002)
Language: English
ISBN-10: 0765302330
ISBN-13: 978-0765302335
Amazon: Beyond the Limit: The Dream of Sofya Kovalevskaya

Beyond the Limit, a novel researched for more than ten years by mathematician and educator Joan Spicci, is the true story of Sofya Kovalevskaya's remarkable personal journey, from the constricted life of a teenage girl in St. Petersburg to the triumph of becoming the first woman to earn a doctorate in mathematics and join the ranks of Europe's great mathematicians of the nineteenth century.

For more than one hundred years, Kovalevskaya's struggle has inspired women of all nations to fight for educational opportunities equal to those available to men. But while she is known for the science and mathematics Opportunity Days sponsored in her name at major universities, the full drama and power of her life has never been told as it now unfolds in this thoroughly researched novel.

Based on Kovalevskaya's own writings, and many other primary sources, the story of her life plays out against a panorama of the turbulent, intellectually challenging 1860s and 1870s, as it follows a brilliant, complex woman on a quest that seems almost impossible to imagine, more than a century later. Friends with some of the intellectual giants of her time, ranging from Dostoevsky to Darwin, she was the equal of them all, as chronicled in this extraordinary work.

In the Russia of the 1860s, young women did as their fathers bid them, and after marriage was arranged, they did what their husbands told them to do. But Sofya Krukovskaya was different. Born to a family in which science and mathematics were already part of its heritage, Sofya takes every opportunity to learn more about mathematics in tutoring sessions. But her tutors know that if she is to realize her potential, she must study at a university. In order to do that, she lies to her family and makes a marriage of convenience with archaeologist Vladimir Kovalevsky, enabling her and her sister Anya to leave Russia and seek education at a German university.

However, leaving Russia is only the first hurdle she must vault to pursue her dream of becoming Europe's first woman mathematician. When she applies for admission, she is refused by stubbornly prejudiced university officials, forcing her to study covertly with the great mathematician Karl Weierstrass, under whose guidance she is at last able to gain her doctorate.

Very close to her sister Anya, a talented writer whose revolutionary fervor takes her to the powder keg of the Paris Commune of 1871, more than once Sofya has to forsake her own goals to save Anya from ruin, and even death.

Married in name only for many years, Sofya and Vladimir have a complex, volatile relationship. Loving each other, they're forced by the needs of their careers to withstand long separations and other trials. Across Europe, through tragedy and finally triumph, their story is richly told against the backdrop of history.

Mathematician and educator Joan Spicci's compelling narrative accurately documents Sofya's educational and professional struggle, in Beyond the Limit.

This fascinating, intimate portrait of Sofya Kovalevskaya's life confronts issues of women's rights and feminism that continue to face women who pursue careers in the sciences in the twenty-first century.

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Comments

( 2 comments — Leave a comment )
jess_faraday
Feb. 10th, 2013 03:25 pm (UTC)
Oh, what an amazing story. I feel the plot bunnies stirring....

Elisa, thank you for sharing these wonderful biographies. They're very inspirational and I do love seeing the different ways people have lived and loved throughout history.
elisa_rolle
Feb. 10th, 2013 03:41 pm (UTC)
I studied her teorema at school, it's amazing to know more about the woman. And yes, I love to find these pieces of "hidden" history.
( 2 comments — Leave a comment )

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