Sonya Kovalevsky, also known as Sophia (Sofia, Sonia) Korin-Kurkovskaya Kovalevskia, grew up a member of Russia’s privileged social class. Her father was a military officer and a land holder; her mother, the granddaughter of a famous Russian astronomer, was an accomplished musician. The family lived comfortably on a country estate, where Sonya, her sister and brother were brought up by a nanny until their education was taken over by governesses and private tutors.
Sonya’s earliest memories of science and mathematics center around a self-educated, eccentric uncle, who told her fairy tales, taught her to play chess. In her autobiography, Sonya recalls that the uncle talked about “squaring the circle, asymptotes, and other things that were unintelligible to me and yet seemed mysterious and at the same time deeply attractive. I have always been taken with various abstract considerations — infinity, for example. It is the philosophical aspect of mathematics which has attracted me all through my life. Mathematics has always seemed to me a science which opens completely new horizons.“ When she was eleven years old, an ill-planned redecorating scheme came up short on wall paper, and Sonya’s bedroom was temporarily papered with the lithographed pages of some old calculus lecture notes from her father’s university days. “I noticed that certain things were shown [on those pages] which I had already heard mentioned by Uncle. It amused me to examine [for hours on end] these sheets of hieroglyphics whose meaning escaped me completely but which, I felt, must signify something very wise and interesting.”
By the age of thirteen Sonya showed an unusual ability and enthusiasm for algebra and geometry. But her father believed that there was no need nor place for learned women, so he put a stop to further mathematical instruction. Secretly, Sonya borrowed an algebra book from one of her tutors and continued to study “under the covers” at night. About a year later a neighbor, who was a professor of science at a nearby school, gave the family a copy of an elementary physics book he’d written. When Sonya tried to read the section on optics, she bumped into trigonometry, a subject she had never heard of. To make sense of some of the derivations, she substituted “a chord for the mysterious sine,” and everything worked for small angles. The neighbor-professor was so impressed that Sonya had independently rediscovered the method by which the concept of sine had developed historically, that he tried to persuade Sonya’s father to arrange serious training in mathematics for her. It took him four years to agree to let her take private lessons in analytic geometry and calculus in St. Petersburg. She mastered these subjects over one winter. Her professor was astounded at the speed with which she assimilated the concepts of calculus, as if she knew them in advance. “In fact, much of the material had long been familiar to me from a formal standpoint [from the walls of my childhood nursery].”
Sonya and her older sister were part of an active young, intelligentsia, who believed in the power of education to hasten a peaceful revolution of the zsarist social structure that would improve humanity’s lot, including equality for women — nineteenth-century Russian universities were closed to women. A few girls managed to study at Swiss and German universities, but even though Sonya wanted desperately to pursue a career as a doctor or chemist (“to be of use”), her family would not allow their single daughters to go abroad. So in 1868 Sonya and her older sister arranged “fictitious marriages” to radical compatriots. Sonya married a promising young paleontologist, Vladimir Kovalevsky, who would contribute to the substantiation of Darwin’s new and controversial theory of evolution, and moved to Heidelberg, Germany to study science and mathematics. (Her sister set off for Paris in search of revolutionary action.) Only then did she discover that university matriculation was not open to women. With persistence she wrung permission to attend lectures on an unofficial basis from the university and spent almost two years studying with some of the foremost scientists in Europe. Sonya’s uncommon mathematical talents made such an impression on her Heidelberg professors that, although she could not earn a degree, they sent her, armed with recommendations, to the most renowned German mathematician of the time, Karl Weierstrass at the University of Berlin.
If Heidelberg was difficult for women, then Berlin was impossible. Women were, without exception, barred from even unofficial or occasional attendance at lectures. Legend has it that, hoping to discourage her, Weierstrass challenged her with a set of problems he had prepared for his more advanced students. She solved them rapidly, and her solutions were clear and original. When Weierstrass ascertained that Sonya’s “personality was [strong enough] to offer the necessary guarantees,” he agreed to teach her privately. He soon came to regard her as the most brilliant and promising of all his students and shared with her not only all his university lectures but also his ideas and unpublished work.
By 1874 Sonya had produced three original works, each one worthy of a Ph.D.: one on the shape of Saturn’s rings; another on elliptic integrals; and the third a pioneering theorem in the general theory of partial differential equations. Since a degree from Berlin was hopeless, Weierstrass presented these dissertations to the University of Göttingen, where there was a precedent for awarding doctorates to foreigners in absentia. In July, 1874 Göttingen, after much saber rattling and based solely on the quality of these three papers, finally awarded to Sonya Kovalevsky the degree of doctor of philosophy in mathematics, summa cum laude. (She had never officially matriculated at any university!)
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 Sonya 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 theater reviewer and science and technology reporter for a St. Petersburg newspaper, and she began work on a novel. For six years Sonya did no new mathematics. During this time she gave birth to a daughter, 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 1883.
In 1880 Sonya 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 mathematical 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 battled obstacles to hiring a woman in Sweden, where it was felt that married women did not need jobs. In the meantime Sonya 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 Sonya, now “respectably” widowed, a probationary position. She accepted, graciously. At Stockholm Sonya began lecturing in German, but after the first year conducted all of her classes in Swedish. She proved to be quite popular with her students, and at the end of six months her probationary status was replaced by an official five-year professorship, and she became an editor of the influential journal Acta Mathematica.
The high point of Sonya’s career came in late 1888, when she won the Prix Bordin, a prestigious prize given by the French Academy of Sciences, for her memoir, 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. This achievement solidified her appointment to a lifetime chair in mathematics at Stockholm in 1889 and a membership in the Russian Academy of Sciences. Although she was the first woman ever elected to the Russian Academy, this was a dubious honor, for she was offered no teaching positions at Russian universities (which she coveted) and, as a woman, she was conspicuously excluded from meetings of the Academy.
Between 1888 and 1891, in addition to her mathematical projects, Sonya completed two novels, collaborated with Mittag-Leffler’s sister on two plays, and wrote numerous newspaper articles on topics ranging from Sweden’s peasant universities to treating hysteria by hypnosis. Sonya died unexpectedly in 1891 from pneumonia following epidemic influenza. The last year of her life was a particularly trying one: she was separated from her daughter, who had been left behind in Moscow; her sister was dying a slow, painful death in Moscow; and a three-year romantic affair came to an end. Sonya’s Swedish friends insisted that she be buried in Stockholm, as one of their own, rather than in her mother Russia. The Russian minister of the interior expressed the opinion that entirely too much attention was being paid to “a woman who was, in the last analysis, a Nihilist [advocate of a 19th-century Russian political party that promoted revolutionary reform].” She is the only woman mathematician to have been commemorated on a Russian postage stamp, though. And, nearly a hundred years after her death, they named a crater on the far side of the Moon after her.
Condensed by Larry Curnutt from “A Russian Childhood” written by Sonya Kovalevsky and translated by Beatrice Stillman, Springer-Verlag, 1978; “Women in Mathematics”, by Lynn Osen, MIT Press, 1974; and “Mr. Sophia’s Pony” by Stephen J. Gould, Natural History, June 1996.