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Sofya Kovalevskaya was a mathematician and writer who made a valuable contribution to the theory of partial differential equations. She was the first woman in modern Europe to gain a doctorate in mathematics, the first to join the editorial board of a scientific journal, and the first to be appointed professor of mathematics.
Background
Sofia Kovalevskaya (née Korvin-Krukovskaya), was born on January 15, 1850 in Moscow, the second of three children. Her father, Vasily Vasilyevich Korvin-Krukovsky, was a man of Polish descent and 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. She was the second child born to the couple; her sister, Anna, was six years older. Five years after her birth, her brother, Fedor, was born. Sophia was raised primarily by a serf nurse named Praskovia. As a child she was nicknamed "Little Sparrow" because she was small and energetic.
When Sophia was eight years old her father, then 59, resigned his commission in the army and moved the family to his country estate in Palibino. At this time he also hired a Polish tutor, Iosif Ignatevich Matevich, and an English governess, Margarita Frantsevna Smith, to supervise his children. In her memoir, Kovalevsky portrays herself as a sad and lonely child who felt unloved. Her sister garnered much attention for being the oldest and her brother was the pride of his parents because he was the only son. However, she eventually developed a special bond with her father and became his favorite child when her intellectual potential became apparent.
Sophia was also close to her father's older brother, Petr Vasilevich Korvin-Krukovsky. He was a well-read man who shared with his niece his political views and knowledge on various subjects, including mathematics. Her introduction to advanced mathematics came as an accident. When the Korvin-Krukovsky family moved to Palibino, they re-decorated their home. When they ran out of wallpaper for the nursery, her father used sheets of old school notes instead. The notes were on differential integral analysis and were her first encounter with calculus.
Education
Sophia struggled against social conventions to get a proper education as a child. Though it was then believed that very young children should not be taught to read, she sat in on her sister's lessons and practiced reading by herself. When her governess limited the number and types of books she was allowed, she sneaked into her father's study to read from his collection. Her formal education was the responsibility of the family tutor, Malevich. He taught her a broad range of subjects from age the time she was 8 until she was 17. She excelled in mathematics. When her father realized this, he instructed her to focus on other subjects. She followed his orders during her tutoring time, but continued to read math books alone at night.
Sophia was allowed to continue her formal mathematics training after she impressed a neighbor with her skills. The neighbor was Nikolai Nikanorovich Tyrtov, a professor of physics at the St. Petersburg Naval Academy. He brought the Korvin-Krukovsky family a copy of a beginning physics textbook as a gift, and she immediately began to read it. She had difficulty understanding it at first because it contained trigonometry, and Malevich was unable to explain the advanced math to her. Through perseverance Sophia figured out the mathematical formulae by herself and finished the book. Tyrtov was impressed by her ability to explain how she figured out the trigonometry. Tyrtov was a strong proponent of higher education for women, and he eventually persuaded the general to allow his daughter to pursue an education in mathematics.
When Sophia was 18, her family moved to St. Petersburg in order to get a better education for her and her brother. Her father hired Alexander Nikolayevich Strannoliubsky, a highly accomplished teacher, as a math tutor. Her remarkable mathematical abilities persuaded Strannoliubsky to become actively involved in promoting women's education in Russia. Eventually he encouraged her to pursue a broader university education. However, Russian universities were closed to women and unmarried women were not allowed to travel abroad, even to study, unless accompanied by a chaperone.
While Sophia was pursuing her scientific interests, her older sister was developing her literary talents and political views, both of which later influenced Sophia's life. Anna began writing as a pastime but eventually secretly published two short stories without her father's permission in a literary journal edited by Fedor and Mikhail Dostoevsky. This led to a brief courtship between Anna and the famous novelist Fedor Dostoevsky, whom Sophia was also very fond of. Anna also became involved in the nihilist movement in Russia. As Koblitz explained in A Convergence of Lives, a nihilist "basically denoted a person who questioned just about everything in traditional tsarist Russia, had great faith in the natural sciences and the power of education, strongly believed in the equality of women, and desired to be of use to the common people in some capacity." Anna's political views influenced her sister, who saw this movement as a means to pursue her education. The sisters decided that the only way to further their education would be for one of them to marry so they could both travel abroad. They planned a "fictitious marriage" whereby a man would agree to the marriage ceremony, but would then let the woman pursue her own life. This was not an unusual arrangement at the time since it was the only way to free a woman from her parents' authority.
The sisters decided that Anna should partake in the fictitious marriage since she was older. However, when the intended husband, nihilist Vladimir Onufrievich Kovalevsky, a publisher of political and scientific works, met the sisters, he was more interested in Sophia because of her intellectual achievements. The couple married in September 1868 and settled in St. Petersburg. Sophia Kovalevsky continued her math lessons with Strannoliubsky but also sat in on classes at the Medical-Surgical Academy. There she befriended a woman who had started her own gynecological practice, and Kovalevsky briefly entertained the idea of a career in medicine. However, she soon realized that mathematics was her true passion.
In order for Kovalevsky to pursue a formal education in mathematics, the newlyweds first moved to Vienna. Kovalevsky was allowed to study physics there, but she could not find a math professor to work with her, so the couple moved to Heidelberg. There, Kovalevsky was allowed to take math courses as well as a variety of other subjects, and her husband studied geology and paleontology. During this time the couple traveled extensively and had social contacts with the leading intellectuals of that time, including Charles Darwin, Thomas Huxley, George Elliot, and Herbert Spencer.
The Kovalevskys soon left Heidelberg to pursue their separate educations. Vladimir moved to Vienna, while Sophia went to Berlin to study with the world-renowned mathematician, Karl Theodore Weierstrass. Weierstrass was reluctant to take Kovalevsky as a student and gave her a test with difficult math problems before agreeing to work with her. He was so impressed by her performance on his test that he tried to get her admitted to the university. He was not successful, so Weierstrass tutored her privately for the next four years. At first he did not consider the possibility of preparing her for a doctorate because he did not believe that married women needed a career. However, when he learned the truth about Kovalevsky's marriage, he changed his mind.
In 1874, Kovalevskaya was granted her doctorate, summa cum laude, from Göttingen University in Germany. Despite this doctorate and letters of strong recommendation from Weierstrass, Kovalevskaya was unable to obtain an academic position. This was for a combination of reasons, but her gender was the major handicap.
Exhausted by the intensity of the last four years of work, the Kovalevskys returned to Russia. Vladimir was unable to find an academic position, and Sofia discovered that the best job she could expect to get was teaching arithmetic at a girls' elementary school. “I was, unfortunately, weak in the multiplication table,” she remarked sarcastically.
Instead she turned to writing, as a theatre reviewer and science and technology reporter for a St. Petersburg newspaper. For six years she neither undertook research nor replied to Weierstrass's letters.
During this time she gave birth to a daughter (in 1878), and she and Vladimir sought their fortune in various business speculations and idealistic fundraising to establish a women's university. These efforts all ended in financial disaster, and the accumulation of frustrations lead to the break-up of their marriage and, eventually, Vladimir's suicide in the spring of 1883.
In 1880, Sofia was persuaded to deliver a paper on some aspect of her work at the Congress of Natural Scientists held in St. Petersburg. In one quick stroke she caught the interest of the conservative Russian scientific establishment and reestablished herself as a mathematician to be taken seriously. Gösta Mittag-Leffler, an ex-student of Weierstrass, was so impressed that for three years he was trying to find a professorship for her in Sweden. In the meantime Sofia moved to Paris and established professional contacts with the most distinguished mathematicians in France. Finally, in 1883, the University of Stockholm, under continued pressure from Mittag-Leffler, offered Sofia, now 'respectably' widowed, a probationary position as a private docent.
After the initial shock of her husband's death, Kovalevskaya immersed herself in mathematical work in an attempt to rid the feeling of guilt. She began to lecture in Stockholm in early 1884, was appointed to an extraordinary five year professorship in June of that year, and in June 1889 became the first woman since the physicist Laura Bassi and Maria Gaetana Agnesi to hold a chair at a European university. During Kovalevskaya's years at Stockholm, she carried out what many consider her most important research. She lectured on the latest topics in analysis and became an editor of the new journal Acta Mathematica. She took over the task of liaison with the mathematicians of Paris and Berlin and took part in the organisation of international conferences. Her status brought her attention from society, and she began again to write reminiscences and dramas that she had enjoyed doing when young.
The high point of Sofia's career came on Christmas Eve of 1888, when she was presented the famous Prix Bordin of the French Academy of Sciences in recognition of her winning memoir Mémoire sur un cas particulier du problème de le rotation d'un corps pesant autour d'un point fixe(On the Problem of the Rotation of a Solid Body about a Fixed Point), in which she completely settled a problem whose solution had long eluded mathematicians.
The rules of the competition for such prizes dictated that each entry be submitted anonymously. The author's name was sealed into an envelope bearing the same motto as that inscribed on the memoir, and the envelope was not to be opened until after the competing work won the prize. So when the jury of the Academy chose Sofia's entry, it was in utter ignorance that the winner was a woman. The brilliance of her entry was judged to be so exceptional that the value of the prize was increased from 3,000 to 5,000 francs “on account of the quite extraordinary service rendered to mathematical physics by this work.” Incidentally, the motto on Sofia's prize-winning essay was 'Say what you know, do what you must, come what may.' This achievement solidified her appointment to a lifetime chair in mathematics at Stockholm in 1889 and a membership in the Russian Academy of Sciences.
Kovalevskaya's further research on this subject won a prize from the Swedish Academy of Sciences in 1889, and in the same year, on the initiative of a famous Russian mathematician Pafnutiy Chebyshev, Kovalevskaya was elected a corresponding member of the Imperial Academy of Sciences. Although the Czarist government had repeatedly refused her a university position in Russia, the rules at the Imperial Academy were changed to allow the election of a woman.
Kovalevskaya's last published work was a short article Sur un théorème de M. Bruns ('On the Theorem by M. Bruns') in which she gave a new, simpler proof of Bruns's theorem on a property of the potential function of a homogeneous body. In early 1891, at the height of her mathematical powers and reputation, Kovalevskaya suddenly died of influenza complicated by pneumonia. Sofia was buried in Stockholm with a white lily wreath dangling from her gravestone from her most cherished friend, Weierstrass.
Sofia Kovalevskaya 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. Although she published only ten papers on mathematics and mathematical physics, many of these included ground- breaking theories or the impetus for future discoveries. Her early work on the theory of differential equations was a particularly valuable contribution to mathematics and led to what is now known as the Cauchy-Kovalevsky theorem for analytic partial differential equations. Kovalevskaya’s other great breakthrough was her paper on the rotation of an unsymmetrical solid body around a fixed point, now known as the Kovalevsky top.
In 1888, she became the first woman to be elected a corresponding member of the Russian Academy of Sciences. In the same year, she was awarded the Prix Bordin of the French Academy of Sciences for a paper on the rotation of a solid body around a fixed point. Kovalevskaya also gained a reputation as a writer, an advocate of women’s rights, and a champion of radical political causes. She composed novels, plays, and essays, including the autobiographical Memories of Childhood (1890) and The Nihilist Woman (1892), a depiction of her life in Russia.
An extraordinary person, Sofia Kovalevskaya was an active advocate of women's rights. It was her struggle to obtain the best education available which began to open universities' doors to women. In addition, her ground-breaking work in mathematics made her male counterparts reconsider their archaic notions of women's inferiority to men in science, thus paving the way for future women scholars to succeed.
Kovalevskaya participated in social movements and shared ideas of utopian socialism. She was involved in the vibrant, politically progressive and feminist movement of late nineteenth-century Russian Nihilism. This involvement caused additional risk in her life, already challenged by the hardships caused by her difficult and underpaid career and exile in various European countries.
Views
Kovalevskaya was inspired by the nihilist movement in Russia, which emphasized the power of education and the equality of women. Kovalevskaya was also an accomplished writer and a strong proponent of higher education for women.
Membership
In 1889, she was made a Corresponding Member of the Russian Academy of Sciences.
Russian Academy of Sciences
,
Russia
Personality
Quotes from others about the person
According to historian of science Ann Hibner Koblitz, Kovalevskaia was "the greatest known woman scientist before the twentieth century".
Historian of mathematics Roger Cooke wrote: "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."
Connections
In 1868, Kovalevskaya entered into a marriage of convenience with a young paleontologist, Vladimir Kovalevsky, in order to leave Russia and continue her studies. In October 1878 their daughter, Sophia Vladimirovna, was born. In 1883, faced with worsening mood swings and the possibility of being prosecuted for his role in a stock swindle, Vladimir committed suicide. In 1889, Kovalevskaya fell in love with 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.
Father:
Lieutenant General Vasily Vasilyevich Korvin-Krukovsky
served in the Imperial Russian Army
Mother:
Yelizaveta Fedorovna Shubert (Schubert)
descended from a family of German immigrants to St. Petersburg
Little Sparrow: A Portrait of Sophia Kovalevsky
Little Sparrow is the first complete biography in any language of Sophia Kovalevsky, the nineteenth-century Russian mathematical genius, champion of equal education for women, and first woman professor of higher mathematics. She pushed the development of analytical mathematics - such as ultraelliptical functions - beyond that of anybody before her. From the French Academy of Science she won an award as important as the later Nobel prize. Sophia Kovalevsky was born January 15, 1850, into the Russian nobility, daughter of a general, descendant on the paternal side from a Hungarian king and on the maternal side from German astronomers. She joined the nihilist movement at age 16. At age 18, in order to escape Russia and study abroad, she obtained parental permission to enter a marriage, which for five years remained platonic. Though a woman, she obtained special permission to study at Heidelberg. When rejected for higher study at Berlin University, she was accepted as a special pupil by the foremost mathematics teacher of the age, Professor Karl Theodore William Weierstrass. After receiving a Gottingen doctorate magnacum laude, in abstentia, she returned to Russia to enter the intellectual life of St. Petersburg, to consummate her marriage, and to bear a daughter. She was a friend of Dostoevsky, Turgenev, George Eliot, and other literary lights of the period, and she wrote an account of her Russian childhood that was considered on a par with Tolstoy's book on his youth. Kennedy's work focuses less on the professional mathematician than on the unusual woman whose life reflects the plight of the female intellectual and scientist in Russia and Europe late in the century.
