Sofia Kovalevskaïa – Mathematician, Author, Astronomer

By Jaime Seltzer

“Say what you know, do what you must, come what may.” – Sofia Kovalevskaïa

Sofia Kovalevskaya was born in 1850 to an upper-class Russian family. Sofia came from a fine and distinguished line of mathematicians, though she did not know it until she had been studying for some time: her grandfather had studied topography, and her great-grandfather was a well-known astronomer.

Sofia did not exactly get an early start on her education. Due to civil unrest, her family moved from their residence in the city to their land in the country. It must have seemed to Sophia’s father that more than just peace and order had fallen by the wayside, since he immediately fired Sofia and her two siblings’ tutor, moved their old nurse to laundry duty, and hired an English governess and a Polish tutor.

The governess dramatically changed Sofia’s life from one of freedom and ignorance to a life of almost comical regimentation with every moment planned out and supervised. Sofia had always loved poetry, but she had to compose in secret, or in her head: her new governess did not approve of poetry, and would pin the poems to the back of her dress and read them dramatically aloud to all comers.

Her work was so ingenious that people began calling her the most brilliant mathematician of her century.

At the same time, Sofia developed a love and reverence for mathematics. When the family ran out of wallpaper for the country house, they pasted Ostográdsky’s lectures on differential equations to the nursery wall! Sofia spent hours gazing at this new, mysterious language, attempting to parse it like some archaeologist before a hieroglyph. Though she felt sometimes invisible to the rest of her family, she was the clear favorite of her father’s oldest brother, Pyotr. Pyotr was an avid reader and researcher, though he was uneducated; and sometimes he would forget who he was talking to, and describe scientific and mathematical matters in great technical detail to little Sofia.

Sofia came to maturity in a time of great upheaval in Russia. On the one hand, her parents were still ensconced in the trappings of high society. On the other, Sofia and her sister and brother were bound to be more proletariat, open-minded and learned. Sofia’s eldest sister maintained a secret correspondence with Dostoyevsky, the famous Russian author and, as a young lady, published stories under a pseudonym, knowing her parents would find her occupation scandalous. Luckily her mother and father relented, and both Sofia and her sister enjoyed a close companionship with the author.

In those days, it was unheard-of for a young lady to leave the country without a man as escort. Adventurous, intellectual young Russian women would sometimes take a husband for the express purpose of leaving the country. Sofia’s older sister wished to do so, and went with Sofia and a friend to inquire of a young intellectual named Vladimir Kovalevsky if he would consent to marry one of them. To their shock, he chose Sofia, six years younger than the other two girls. Since Sofia’s older sister was not married, there was little chance of her father agreeing to the match: therefore, Sofia tricked him by pretending to be off engaging in romantic shenanigans with Vladimir while the entire extended family was present. As a result, her father was forced by the threat of shame to state that the pair were engaged!

The match was not romantic, however: the young man treated Sofia more like a little sister than a wife. When they emigrated to Petersburg, and later to Heidelberg, they had very little to do with one another, pursuing their own respective educations, Sofia in mathematics and Vladimir in geology. Sofia had to get special permission to study in Heidelberg, since women were not allowed into the college at that point; but she had already faced so many trials in order to study that this news barely gave her pause. She learned mathematics privately, from the calculus professor Karl Weierstrass. She completed three papers over four years’ study, all of which Weierstrass claimed were equal to a thesis for a doctoral degree. The University of Göttingen agreed, presenting it to her in the absence of a defense (since, after all, she had never technically attended.) She was the first woman in Germany to ever apply for a doctoral degree in mathematics.

Sofia Kovalevskaya

Sofia Kovalevskaya and her card in the Women in Science game.

Sofia’s three papers were all equally groundbreaking. The first was called On the Theory of Partial Differential Equations, which extrapolated the next step in a famous theorem proposed by Cauchy. The theorem is now called the Cauchy-Kovalevsky Theorem after Sofia and can help describe, among other things, the diffusion of heat through a system.

Her second paper was about Abelian and elliptic integrals (another topic recently addressed by Cauchy), and the third was about Saturn’s rings. She used mathematics to demonstrate that Saturn’s rings were of an elliptical shape, with one common, central point.

After her doctorate had been obtained and the intellectual scramble was over, Sofia found herself at loose ends. She and Vladimir had developed romantic affection for one another, and traveled for a while before returning to Russia. Sofia thought she would sit for a master’s degree in order to teach, but was told that since women were barred from teaching in higher education, she shouldn’t bother. One official made her position quite plain, telling Sofia that the best she could hope for was to teach elementary students arithmetic. Instead, Sofia helped design curriculum for higher mathematics courses, but when she offered to teach one at St. Petersburg, they turned her down. Meanwhile, she wrote short stories, novels, and newspaper articles to keep herself occupied. Her work was generally well-received and her account of her own life, Recollections of Childhood is at once stirring, comical, and charming.

Finally, she was asked to present the work of her second doctoral dissertation at the Congress of Russian Naturalists and Physicians, where it was favorably received. Mittag-Leffler, a well-known mathematician of the time, became determined to secure her a teaching post in Europe if not in Russia. Sofia, heartened by the support, began once more to work with Weierstrass, believing that it would strengthen her position as a potential professor. She worked on mathematics that described the refraction of light through crystals.

Sofia’s father passed away and left her a small inheritance which Vladimir invested… unfortunately quite unwisely. In 1883, Vladimir realized that he had been cheated out of his and his family’s life savings and that had been implicated in theft because he had lent his money to unscrupulous characters. He also appears to have suffered from manic and depressive episodes. He eventually took his own life.

Sofia buried herself in her work, finally achieving a professorship at the University of Stockholm in 1889 much to her relief – she was still paying off the debts that Vladimir had incurred in his final illness. She completed a paper called On the Rotation of a Solid Body about a Fixed Point, which had applications regarding the rotation of asymmetrical objects where the center of mass is not within the object – a type of object now called a Kovalevskaya Top. Her work was so ingenious that people began calling her the most brilliant mathematician of her century.

Sofia also championed women’s rights. She was the first female member of the Russian Academy of Sciences, and the first woman since Laura Bassi and Maria Gaetana Agnesi in the 1700s to hold a chair at any European University. She was an editor for the journal Acta Mathematica, and her paper on rotation earned her the Prix Hordin prize, which was elevated from 3,000 to 5,000 francs because her math was just that ingenious. Despite publishing only ten papers over the course of her career, the percentage of fascinating and groundbreaking ideas she presented is remarkable.

References:
Cooke, R., & Barile, M. (2007). Kovalevskaya, Sofia (1850-1891). In Eric Weisstein’s World of Biography. Retrieved from http://scienceworld.wolfram.com/biography/Kovalevskaya.html
European Commission, The. (2015). Sofia Kovalevskaya – The right equation. In Epigenesys. Retrieved from http://www.epigenesys.eu/en/science-and-you/women-in-science/739-sofia-kovalevskaya
Sofya Vasilyevna Kovalevskaya. (2015). In Encyclopædia Britannica. Retrieved from http://www.britannica.com/biography/Sofya-Vasilyevna-Kovalevskaya

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