|
|
|
SOFIA VASILYEVNA KOVALEVSKAYA |
| Sofia Kovalevskaya was the middle child of
V. Korvin-Krukovsky, an artillery general, and
Yelizaveta Shubert, both well-educated members of the Russian nobility. Sofia was educated by
tutors and governesses, lived first at Palabino, the Krukovsky country estate, then in St.Petersburg, and joined her family's social circle which included the author
Dostoevsky. Sofia was attracted to mathematics at a very young age. Her uncle Pyotr Vasilievich Krukovsky,
who had a great respect for mathematics, spoke about the subject. When Sofia was 11 years old, the walls of her nursery were papered with pages of Ostrogradski's
lecture notes on differential and integral analysis. She noticed that certain things on the
sheets she had heard mentioned by her uncle. Studying the wallpaper was Sofia's introduction to
calculus. It was under the family's tutor, Y I Malevich, that Sofia undertook her first proper study of
mathematics, and she started to neglect other studies. Sofia 's father decided to put a stop to her
mathematics 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
formulas 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. Sofia was forced to
marry so that she could go abroad to enter higher education. 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. At the age
of eighteen, she entered a nominal marriage with Vladimir Kovalevski, a young palaeontologist.
This marriage caused problems for Sofia and, throughout its fifteen years, it was a source of
intermittent sorrow, exasperation and tension and her concentration was broken by her frequent
quarrels and misunderstandings with her husband. In 1869 Sofia travelled 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 obtain
the permission of each of her lecturers. Sofia studied there successfully for three semesters
and, according to the memoirs of a fellow student, she immediately attracted the attention of her teachers with her uncommon mathematical ability.
In 1871 Kovalevskaya moved to Berlin to study with Weierstrass, Konigsberger's teacher. Despite
the efforts of Weierstrass and his colleagues the senate refused to permit her to attend courses
at the university. Ironically this actually helped her since over the next four years
Weierstrass tutored her privately.
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 Gottingen University.
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 sex was a
major handicap. Her rejections resulted in a six year period during which time she neither
undertook research nor replied to Weierstrass's letters. She was bitter to discover that the
best job she was offered was teaching arithmetic to elementary classes of school
girls. In 1878, Kovalevskaya gave birth to a daughter, but from 1880 increasingly returned to her
study of mathematics. In the spring of 1883, Vladimir, from whom Sofia had been separated for two years, committed
suicide. After the initial shock, Kovalevskaya immersed herself in mathematical work in an
attempt to rid herself of feelings of guilt. Mittag-Leffler managed to overcome opposition to
Kovalevskaya in Stockholm, and obtained for her a position as privat docent. She began to
lecture there in early 1884, was appointed to a five year extraordinary 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 taught courses 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 topic of the Prix Bordin of the French Academy of Sciences was announced in 1886. Entries
were to be significant contributions to the problem of the study of a rigid body. Kovalevskaya
entered and, in 1886, was awarded the Prix Bordin for her paper
. In recognition of the brilliance of this work the prize money was raised from 3,000 to 5,000 francs. 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 Chebyshev, Kovalevskaya was elected
a corresponding member of the Imperial Academy of Sciences. Although the Tsarist government had
repeatedly refused her a university position in her own country, 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 theoreme de M. Bruns in which she
gave a new, simpler proof of Bruns' 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 died of influenza complicated by pneumonia. Article by: J J O'Connor and E F Robertson |
|
|
|
