sofia kovalevskaya

Sofia Kovalevskaya was the middle child of Vasily Korvin-Krukovsky, an artillery general, and Yelizaveta Shubert, both well-educated members of the Russian nobility. Sofia was educated by tutors and governesses first at Polibino, the Krukovsky family country estate, near Pskov, then in St. Petersburg. She joined her family's social circle which included Dostoevsky (who even proposed to her elder sister Anna, but was rejected).

Sofia was attracted to mathematics at a very young age. Her uncle Pyotr Krukovsky was not the brightest or most educated man, but he had a passion for mathematics and told Sofia about squaring a circle and asymptotes, even before she was old enough to know what these words meant.

When Sofia was 11 years old, the walls of her nursery were temporarily (for a shortage of wallpaper) papered with pages of Ostrogradsky's lecture notes on differential and integral analysis from her father's university days. She noticed that certain things on the sheets she had heard mentioned by her uncle.

Fascination with maths

It was under the family's tutor Josef Malevich that Sofia undertook her first proper study of mathematics, and she says that it was as his pupil that she began to feel an attraction for mathematics so intense that she started to neglect other studies.

Sofia’s father decided to put a stop to her math lessons, but she borrowed a copy of Bourdeu's Algebra, which she read at night when the rest of the household was asleep. A year later a neighbour, Professor Tyrtov, presented her family with a physics textbook which he had written, and Sofia attempted to read it. 

She did not understand the trigonometric formulae and attempted to explain them herself. Tyrtov realised that in her working with the concept of sine, she had used the same method by which it had developed historically. Tyrtov argued with Sofia's father that she should be encouraged to study mathematics further but it was several years later that he permitted Sofia to take private lessons.

Marriage and family life

Sofia was forced to marry so that she could go abroad to enter higher education, as Russian universities in the 19th century were closed to women. Her father would not allow her to leave home to study at a university, and women in Russia could not live apart from their families without the written permission of their father or husband. 

Meanwhile, Sofia and her elder sister Anna were part of an active young intelligentsia, who believed in the power of education to hasten a peaceful revolution of the tsarist social structure that would improve human nature, and to provide equal rights for women. So in 1868 the two sisters arranged fictitious marriages to radical compatriots. 

Sofia married Vladimir Kovalevsky, a promising young paleontologist. This marriage caused problems for Sofia and, throughout its 15 years, it was a source of intermittent sorrow, exasperation and tension. Her concentration was broken by her frequent quarrels and misunderstandings with her husband.

University studies in Europe

In 1869 Sofia traveled to Heidelberg to study mathematics and the natural sciences, only to discover that women could not matriculate at the university. Eventually she persuaded the university authorities to allow her to attend lectures unofficially, provided that she obtains the permission of each of her lecturers. 

Sofia studied there successfully for three semesters and, according to the memoirs of a fellow student, immediately attracted the attention of her teachers with her mathematical ability. Professor Königsberger, the eminent chemist Kirchhoff, and all of the other professors were ecstatic over their gifted student and spoke about her as an extraordinary phenomenon.

In 1871 Kovalevskaya moved to Berlin to study with Weierstrass, Königsberger's teacher. Despite the efforts of Weierstrass and his colleagues, she was not permitted to attend courses at the university. Ironically this actually helped her since over the next four years Weierstrass tutored her privately. 

Doctorate degree

By the spring of 1874, Kovalevskaya had completed three papers. Weierstrass deemed each of these worthy of a doctorate. The three papers were on partial differential equations, Abelian integrals and Saturn's Rings. The first of these is a remarkable contribution which was published in Crelle's Journal in 1875. The paper on the reduction of Abelian integrals to simpler elliptic integrals is of less importance, but it consisted of a skilled series of manipulations which showed her complete command of Weierstrass's theory.

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.

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