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.
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