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Sonya Kovalevskaya


From: Anonymous
Date: Sun, 19 Nov 1995 13:22:55 -0500
Subject: Sonia Cavalski?

Could you please advise me on where I can find information on a 
mathematician by the name of Sonia Cavalski. I am not sure on the 
spelling of the last name.

Thanks, Rena


Date: Sun, 19 Nov 1995 14:16:06 -0500
From: Sarah Seastone
Subject: Re: Sonia Cavalski?

Hi Rena,

You're probably thinking of Sonya Kovalevskaya (1850-1891).

You can find lots of math history sites from our Internet Mathematics
Library on the Web at http://mathforum.org/library/   .  Check 
out

   http://mathforum.org/library/browse/static/topic/history.html   

In case you don't have World Wide Web access, here's some information on
Sonya Kovalevskaya from the Women Mathematicians site at

   http://www.scottlan.edu/lriddle/women/alpha.htm    - specifically
   http://www.scottlan.edu/lriddle/women/kova.htm   

Written by Becky Wilson, Class of 1997 (Agnes Scott College)

An extraordinary woman, Sonya Kovalevskaya was not only a great
mathematician, but also a writer and advocate of women's rights in the 
19th century.  It was her struggle to obtain the best education 
available which began to open doors at universities to women.  In 
addition, her ground-breaking work in mathematics made her male 
counterparts reconsider their archaic notions of women's inferiority to 
men in such scientific arenas.

Sonya Krukovsky Kovalevskaya was born in 1850.  As the child of a
Russian family of minor nobility, Sonya was raised in plush 
surroundings.  She was not a typically happy child, though.  She felt 
very neglected as the middle child in the family of a well admired, 
first-born daughter, Anuita, and of the younger male heir, Fedya.  For 
much of her childhood she was also under the care of a very strict 
governess who made it her personal duty to turn Sonya into a young lady. 
As a result, Sonya became fairly nervous and withdrawn--traits which 
were evident throughout her lifetime (Perl 127-128).

Sonya's exposure to mathematics began at a very young age.  She claims 
to have studied her father's old calculus notes that were papered on her 
nursery wall in replacement for a shortage of wallpaper.  Sonya credits 
her uncle Peter for first sparking her curiosity in mathematics.  He 
took an interest in Sonya and made time to discuss numerous abstractions 
and mathematical concepts with her (Rappaport 564).  When she was 
fourteen years old she taught herself trigonometry in order to 
understand the optics section of a physics book that she was reading. 
The author of the book and also her neighbor, Professor Tyrtov, was 
extremely impressed with her capabilities and convinced her father to 
allow her to go off to school in St. Petersburg to continue her studies 
(Rappaport 564).

After concluding her secondary schooling, Sonya was determined to 
continue her education at the university level.  However, the closest 
universities open to women were in Switzerland, and young, unmarried 
women were not permitted to travel alone.  To resolve the problem Sonya 
entered into a marriage of convenience to Vladimir Kovalevsky in 
September 1868.  The couple remained in Petersburg for the first few 
months of their marriage and then traveled to Heidelburg where Sonya 
gained a small fame.  People were enthralled by the quiet Russian girl 
with an outstanding academic reputation (Perl 131).

In 1870, Sonya decided that she wanted to pursue studies under Karl
Weierstrass at the University of Berlin.  Weierstrass was considered one 
of the most renowned mathematicians of his time, and at first he did not 
take Sonya seriously.  Only after evaluating a problem set he had given 
her did he realize the genius at his hands.  He immediately set to work 
privately tutoring her because the university still would not permit 
women to attend.  Sonya studied under Weierstrass for four years.  She 
is quoted as having said, "These studies had the deepest possible 
influence on my entire career in mathematics.  They determined finally 
and irrevocably the direction I was to follow in my later scientific 
work: all my work has been done precisely in the spirit of Weierstrass" 
(Rappaport 566).  At the end of her four years she had produced three 
papers in the hopes of being awarded a degree.  The first of these, "On 
the Theory of Partial Differential Equations," was even published
in Crelle's journal, a tremendous honor for an unknown mathematician
(Rappaport 566).

In July of 1874, Sonya Kovalevskaya was granted a Ph.D. from the
University of Gottingen.  Yet even with such a prestigious degree and 
the help of Weierstrass, who had grown quite fond of his pupil, she was 
not able to find employment.  She and Vladimir decided to return to her 
family in Palobino.  Shortly after her return home, her father died 
unexpectedly.  It was during this period of sorrow that Sonya and 
Vladimir fell in love.  Their marriage produced one daughter (Perl 133). 
While at home, Sonya neglected her work in mathematics but instead 
developed her literary skills.  She tried her hand at fiction, theater 
reviews, and science articles for a newspaper (Rappaport 567).

In 1880, Sonya returned to her work in mathematics with a new fervor. 
She presented a paper on Abelian integrals at a scientific conference 
and was very well received.  Once again she was faced with the dilemma 
of finding employment doing what she loved most--mathematics.  She 
decided to return to Berlin, also home to Weierstrass.  She was not 
there long before she learned of Vladimir's death.  He had committed 
suicide when all of his business ventures had collapsed.  Sonya's grief 
threw her into her work more passionately than ever (Perl 134).

Then, in 1883, Sonya's luck took a turn for the better.  She received an
invitation from an acquaintance and former student of Weierstrass, Gosta
Mittag-Leffler, to lecture at the University of Stockholm.  In the 
beginning it was only a temporary position, but at the end of a five 
year period, Sonya had more than proven her value to the university. 
Then came a series of great accomplishments.  She gained a tenured 
position at the university, was appointed an editor for a mathematics 
journal, published her first paper on crystals, and in 1885, was also 
appointed Chair of Mechanics.  At the same time, she co-wrote a play, 
"The Struggle for Happiness," with friend, Anna Leffler (Rappaport 568).

In 1887, Sonya again received devastating news. The death of her sister,
Anuita, was particularly hard on Sonya because the two had always been
very close. Fortunately, it was not long afterward that Sonya achieved 
"her greatest personal triumph" (Perl 135). In 1888, she entered her 
paper, "On the Rotation of a Solid Body about a Fixed Point," in a 
competition for the Prix Bordin by the French Academy of Science and 
won. "Prior to Sonya Kovalevsky's [Sonya Kovalevskaya] work the only 
solutions to the motion of a rigid body about a fixed point had been 
developed for the two cases where the body is symmetric" (Rappaort 569). 
In her paper, Sonya developed the theory for an unsymmetrical body where 
the center of its mass is not on an axis in the body. The paper was so 
highly regarded that the prize money was increased from 3000 to 5000 
francs.

Also at this time, a new man entered her life.  Maxim Kovalevsky came to
Stockholm for a series of lectures. There he met Sonya, and the two had 
a scandalous, rocky affair.  The basic problem was that they were both 
too passionate about their work to give it up for the other. Maxim's 
work took him away from Stockholm and he wanted Sonya to give up her 
hard-earned positions to simply be his wife. Sonya flatly rejected such 
an idea but still could not bare the loss of him.  She remained in 
France with him for the summer and fell into another one of her frequent 
depressions.  Again, she turned to her writing.  While she was in 
France, she finished Recollections of Childhood (Perl 136).

In the fall of 1889, she returned to Stockholm.  She was still miserable 
at the loss of Maxim even though she frequently traveled to France to 
visit him.  She eventually became ill with depression and pneumonia.  On 
February 10, 1891, Sonya Kovalevskaya died and the scientific world 
mourned her loss.  During her career she published ten papers in 
mathematics and mathematical physics and also several literary works. 
Many of these scientific papers were ground-breaking theories or the 
impetus for future discoveries.  There is no question that Sonya 
Krukovsky Kovalevskaya was an incredible person. The President of the 
Academy of Sciences, which awarded Sonya the PrixBordin, once said: "Our 
co-members have found that her work bears witness not only to profound 
and broad knowledge, but to a mind of great inventiveness" (Rappaort 
569).

Perl, Teri. "Sonya Kovalevskaya." Math Equals: Biographies of Women
Mathematicians and Relates Activities. United States and Canada:
Addison-Wesley Publishing Co., 1978: 127-137.

Rappaport, Karen D. "S. Kovalevsky: A Mathematical Lesson." The
American Mathematical Monthly 88 (October 1981): 564-573.

 - Doctor Sarah, The Geometry Forum 

    
Associated Topics:
High School History/Biography

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