Q: Today we have the
privilege of speaking with renowned mathematician Sofia

Vasi…Vasilyev…V-A-S-I-L-Y-E-V-N-A
K-O-V-A-L-E-V-S-K-A-Y-A. Sorry about that Sofia.

A: It’s alright. That happens a lot.

Q: You have had kind of a tough life, haven’t you?

A: Yes, I suppose so. But when all was said and done,
I believe I did fairly well for myself.

Q: I agree. Now, would you like to tell us a little
about your background?

A: Certainly. I was born on the fifteenth of January
in the year of 1850 in Moscow, Russia. I lived for most of
my childhood on my family’s country estate, Palabino.
My father, Vasily Korvin-Krukovsky, was an artillery general and
a nobleman. My mother, Velizaveta Shubert, was of noble
blood as well. That could be a reason as to why my sister,
Anuita, and I were allowed to be tutored in our childhood.
My father was a good man, and I his favorite child, but I’m
afraid he and Anuita did not always get along. I believe my
father’s idea of an educated woman was quite different from
hers. The difference between Anuita and I was that Anuita
was more concerned with behaving like a contemporary woman,
whereas I was more concerned with being educated like one.
I suppose I had more of an intellectual curiosity about me than a
thirst for freedom.

Q: At what point did mathematics begin to interest you?

A: I must have been about nine years old when I bit a
playmate who kept me from talking science with my Uncle
Fedor. He and my Uncle Petr were the only two adults ever
willing to indulge me in intelligent conversation. When I
was 11, Ostrogradski’s notes on differential and integral
analysis papered the walls of my nursery. It captivated me.

Q: Your father supported this?

A: Actually, he began to notice that my other studies were
suffering, and he forbade my mathematical studies. Luckily
for me, a neighbor was a professor of physics at the Petersburg
Naval Academy, and brought me a text with beginning trigonometric
functions in it. I began to teach it to myself. When
next he came, he didn’t believe that I understood. But
I explained my method, which was that in this unit circle, or
this circle with the radius of one, the chord value was close
enough to the sine value, or height of the drawn triangle, to
substitute for sine. That was how I made sense of it.
He was very excited, and said that this was the reasoning used in
the development of trigonometry. He persuaded my father to
allow me to take lessons in trigonometry and calculus.

Q: When you got older, which were the most important of the
courses you took? Didn’t you have problems getting
into classes because of your gender?

A: Yes, I had many problems because I was a woman.
Because the concept of marriage for convenience had just recently
been introduced, I married Vladimir Kovalevsky when I was
18. Although this later turned out unpleasantly, it enabled
my sister and I to go to Germany. I remained in Heidelberg
when Anuita left for Paris and Vladimir for Vienna, but I then
discovered that I was not allowed to attend the university.
Eventually I was able to attend classes unofficially, and after
two years I was able to study with Professor Karl Weierstrauss at
the University of Berlin. Eventually I wrote three original
works. On the Theory of Partial Differential Equations and
On the Reduction of a Definite Class of Abelian Integrals of the
Third Range were both about mathematics. My third work,
Supplementary Research and Observations on Laplace’s
Research on the Form of the Saturn Ring, was on astronomy.

Q: Could you briefly try to explain the theories in these
three works?

A: On the Theory of Partial Differential Equations
addressed a system of differential equations of the first order
in n variables. Basically, in this world, there can be a
situation, if you will, such as atmospheric temperature, that is
a function of several factors, or variables. The effect of,
say…time, on atmospheric temperature, is a partial
derivative (the rate of change of the function with respect to
one of the variables.) The function changes as one variable
changes and the other remains constant. In keeping with the
example, a partial derivative would be the change in atmospheric
temperature with time progression, while latitude, longitude, and
altitude remain the same. Partial differential equations
are equations involving partial derivatives. I proved that
under certain conditions, there exists one and only one solution
to a given partial differential equation. On the Reduction
of a Definite Class of Abelian Integrals was concerning the
classical problem of the revolving of a solid body around a fixed
point, for example, a pendulum or a top. I had always felt
that these problems could be solved with the help of abelian
integrals, or functions defined using certain types of definite
integrals. They were almost generalizations of
trigonometric functions. Anyway, I solved the problem using
these abelian integrals, and apparently there were three
classical cases involving this solid body, and I solved the most
difficult. My last dissertation paper, the one on
astronomy, was on the reduction of abelian integrals to simpler
elliptic integrals. On the topic of Saturn’s rings,
which I assumed were liquid, I elaborated on the theories of
previous mathematicians, including Laplace. He theorized
that the rings were ellipsoidal, whereas I believed that they
were more egg-shaped, ovoid, and positioned or oriented in a
specific way. There’s good news and bad news about
this last paper; yes, I was right about the shape of
Saturn’s rings. Unfortunately, since I assumed the
rings were liquid and they are actually gaseous, this is little
more than a coincidence. Oh well!

Q: That’s very impressive. Now, I know that you
never were able to find a position teaching at a university for
some time. But didn’t you get a degree of some sort
from the University of Gottingen?

A: Yes, I got a degree of a Doctor of Philosophy in
Mathematics, summa cum laude, based on my three papers, without
any examination or public defense. I was also able to read
my paper on abelian integrals to the Sixth Congress of Natural
Sciences in Petersburg, in 1880. In 1883, I was finally
offered a position by my friend Gosta Mittag-Leffler at the
University of Stockholm, in Sweden. I also won the Prix
Bordin, which was a contest for solving the problem of the
differential equations involved in the rotation of a solid body
around a fixed point, which you know I was already actively
involved in. That was very hard however, as by that time my
husband had committed suicide and my sister Anuita died of
complications from an operation. The deadline of the
contest drove me forward. Luckily, mathematics was more of
a release at that point than my work.

Q: I’m sorry to hear about your husband and
sister. Now for my last question. Of all the people
you’ve worked with, which ones have helped you most?

A: Well, I would have to say my first calculus teacher, A.N
Strannoliubskii, who not only aided my mathematic development,
but also supported my and other women’s academic
progress. He was a truly enlightened man. Another
great friend and colleague was Karl Weierstrauss, who taught me
privately when I was not allowed to attend classes at Berlin, and
collaborated with me on my papers. Gosta, whom I mentioned
before was also a dear friend. And I should really mention
poor Vladimir. As unpleasant as our marriage became, he did
marry me with the intention of helping to liberate my sister and
I. He did not mean for it to become the situation it did.

Q: Well, thank you for your time, Sofia. It was nice
to speak with such an example of a woman pioneering in the
male-dominated world of educated 19th century Russia.

A: Thank you. And a shout out to Karlo, Gost-meister,
and all my other homies. Peace out y’all.

Works Cited

Koblitz, Ann Hibner. __A Convergence of
Lives__. New Jersey: Rutgers University Press, 1993

A really good source, because it breaks down the math really well, and gives insight into her character.

Morrow, Charlene, and Teri Perl. __Notable
Women in Mathematics: A Biographical Dictionary__ .
Connecticut: Greenwood Press, 1998

A good source for a brief overview-not the source for detail, which you need sometimes.

www-history.mcs.st-andrews.ac.uk/history/mathematicians/kovalevskaya.html

A good source to mark the milestones of Kovalevskaya’s career. It hit all the highpoints.