Sofia Kovalevskaya

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.