S. Kovalevsky: A Mathematical Lesson

Sofya Kovalevsky was a noted writer whose works include both fiction and nonfiction. She was also a political activist and a public advocate of feminism. In addition, she was a brilliant mathematician who made significant contributions despite the enormous educational and political obstacles that she had to overcome. Somehow her many achievements have been forgotten. In those few instances where her work has not been lost it has been denigrated by such studies as Felix Klein's history of nineteenth-century mathematics. Klein dismisses Kovalevsky's work in the following manner: works are done in the style of Weierstrass and so one doesn't know how much of her own ideas are in them.' He finds something wrong with all her research and credits her with only one positive accomplishment, drawing Weierstrass out of his shell through their correspondence. is time to set this record straight and to let the facts speak for themselves. Sofya Krukovsky, known affectionately as Sonya, was born in Moscow in 1850. Her father, a Russian army officer, retired in 1858 and moved the familySofya, her older sister, Anyuta, and her younger brother, Fedyato Palibino, an estate near the Lithuanian border. After settling at Palibino, the household discovered that they had not brought a sufficient amount of wallpaper with them. Rather than travel a great distance to obtain new wallpaper, they decided to use old newspapers on the wall. Since only the nursery required the paper, this was deemed an adequate solution. However, while searching the attic for newspaper, they discovered paper of a better quality. On it were the lecture notes from a calculus course taken by General Krukovsky. This is how the nursery walls came to be covered with the calculus notes that, in her later years, Sofya claimed to have studied. Sofya often repeated this anecdote and enjoyed reporting how her calculus teacher exclaimed: You have understood them as though you knew them in advance.2 Kovalevsky claimed that her interest in mathematics was aroused by her Uncle Peter, who would discuss numerous abstractions and mathematical concepts with her. When the family tutor, Joseph Malevich, read of this in Sofya's autobiographical work, Memories of Childhood, he was incensed. He wrote a long essay in a Russian newspaper explaining why he should receive credit for Kovalevsky's mathematical development. In response to this criticism Kovalevsky wrote the following tribute in An Autobiographical Sketch: It is to Joseph Malevich that I am indebted for my first systematic study of mathematics. happened so long ago that I no longer remember his lessons at all.... was arithmetic that Malevich taught best.. .I have to confess that arithmetic held little interest for me.3 Kovalevsky4 studied mathematics against her father's wishes. When she was thirteen, she smuggled an algebra text into her room and studied it. When she was fourteen she taught herself trigonometry in order to study a physics book written by her neighbor Professor Tyrtovtrigonometry was necessary for the optics section, and the young Sofya taught herself without tutor or text. By constructing a chord on a circle, she was able to explain the sine function and to develop the other trigonometric formulas. When Professor Tyrtov saw her work, he was struck by its similarity to the actual mathematical development. Calling her a new Pascal, Tyrtov pleaded with the General to permit Sofya to study mathematics. After a year of exhortation, General Krukovsky relented and allowed Sofya to go to Petersburg to study calculus and other subjects. After completing her studies in 1867, Sofya wanted to continue her education, but the Russian university system was closed to women. The only option for study was to go to Switzerland, but General Krukovsky would not allow his daughters to go abroad.