# Biographies of Great Mathematicians

# Sonya Kovalevski (1850-1891)

Excerpt from from Math Odyssey 2000

Sonya Kovalevsky (nee Krukovsky) has been described as the brightest star among all female mathematicians since the time of Hypatia (4th century AD). Her work in the field of analysis is a permanent monument to her greatness. The Cauchy-Kovalevsky Theorem is at the foundation of most graduate courses in partial differential equations. Her novel The Sisters Rajevski (based upon her own childhood) is a superb account of life among the intellectuals at a crucial period in Russian history.

When she was fifteen and beginning to study mathematics, she and her sister had been introduced into an elite circle of European intellectuals living in Moscow. Her sister Anuita had published a short story in a magazine edited by Fyodor Dostoevsky. Sonya, being very talented in literature as well as mathematics wanted to excel in both fields, and was eager to enter university study. She also had a strong interest in studying medicine and physics, all at the age of 15. Unfortunately, the Russian universities had been closed to women since 1863, reversing a liberal movement in Russia of just a few years before.

Sonya's father didn't mind that his daughter was studying calculus under a private tutor at the naval school in St. Petersburg, but he was against having her pursue mathematics as a serious career, so he was unwilling to send her abroad to study. In any case, unmarried women in this level of Russian society were not free to travel alone.

Since higher education was denied such women in Russia at the time, a new style of marriage became the fashion-- "platonic" marriages for intellectual convenience. In many cases, the young married couple could take along a family member as a traveling companion. This was the method taken by Sonya and her sister in 1868. When Sonya was 18, she married Vladimir Kovalevsky.

By now Sonya came to realize that she could not learn everything, so she settled on mathematics as her first love. She and her new husband went off to Heidelberg -- Vladimir to study paleontology and Sonya to study higher mathematics. (Later Vladimir went his own way leaving her in Heidelberg.) She had to get special permission to attend lectures at the University, but she was such a brilliant student that she easily won over all her professors and had no trouble attending any class she wanted.

After two years, she went to Berlin to study with the great German mathematician Karl Weierstrass. But when she got there she found out that the University of Berlin did not allow women to attend lectures. She brought excellent references from Heidelberg and was hoping to be able to study privately with Weierstrass. He decided to quickly dispatch her by sending her away with a set of very difficult problems that he had prepared for some of his more advanced students. He was thoroughly convinced that she would fail and gave the matter no further thought.

To his astonishment she came back a week later with correct solutions to all the problems. Not only were they correct, but also clear, original and some cases, brilliant. Weierstrass immediately made every effort to get permission for her to attend lectures; he was unsuccessful, so he offered to meet with her privately and share his lecture notes with her.

She worked with him for the next four years and received her doctorate in 1874. By the time she got her degree, Sonya had published several original papers in the field of higher mathematical analysis and applications to astronomy and physics. Now she was a significant researcher and expositor of mathematics, but she was still a woman and, therefore, unable to find a job in academia.

Weierstrass tried to find her an academic position worthy of her talents, but his every effort was blocked by bigotry and an unyielding attitude concerning women. When she could find no market for her mathematical training she got back together with her husband and began a life as poet, theatrical critic, novelist, wife and mother. But she could not stay away from mathematics and began looking for a job again.

Her daughter was less than one year old in 1879 when Sonya again left her husband and moved back to Berlin, then to Paris. She continued to publish papers in the application of mathematics to physics and finally in 1883 she was able to obtain a position in the University of Stockholm as a lecturer on the theory of partial differential equations.

Sonya's greatest success in mathematics occurred in 1888 when she won the Prix Bordin of the French Academy of Sciences for her paper On the Problem of the Rotation of a Solid Body about a Fixed Point. She won this prize despite the fact that she was a woman and this is how it happened. The rules of the Academy provided that the papers submitted for this honor had to be anonymous, so the judges were unaware that they had selected a paper that was authored by a woman. Actually, her paper was so impressive that the judges decided to double the prize.

Her mathematical and teaching abilities earned her a permanent tenured position at Stockholm after she won the French prize. The next year Sonya was awarded a prize by Stockholm Academy of Sciences for two more papers, and later that year she was elected, as the first woman member, to the Russian Academy of Sciences, at last receiving recognition in her own country. During the next two years before her death in 1891, she wrote The Sisters Rajevsky and another novel Vera Vorontzoff - both received high praise from literary critics, who were surprised at her versatility. To which she replied:

I understand your surprise at my being able to busy myself simultaneously with literature and mathematics. Many who have never had an opportunity of knowing any more about mathematics confound it with arithmetic, and consider it an arid science. In reality, however, it is a science which requires a great deal of imagination, and one of the leading mathematicians of our century states the case quite correctly when he says that it is impossible to be a mathematician without being a poet in soul.

EXERCISES

1. In addition to her great success in mathematics, Sonya Kovalevsky has been praised for her work in what other intellectual activity ?

2. What French prize was awarded to her and what were some of the unusual events associated with it?

3. What trick did Sonya and her sister Anuita use in order to be able to leave Russia for study abroad and where did she go?

What famous mathematician gave her private lessons in Berlin, and why?