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Sofia Krukovsky

By Michelle Thaller

January 2000

Dr. Michelle Thaller is an outreach scientist at the SIRTF Science Center at the California Institute of Technology.

IHARDLY HAD TIME to notice while I was working on my dissertation, but all of the old
UNIX machines in the Georgia State University astronomy department were named after lesserknown
historical astronomers. My advisor’s machine was Plaskett (he was, after all, a massive
star specialist), while the professor next door had Hogg. There were some female names too — like
Hypatia, whom I remembered from Carl Sagan’s “Cosmos” TV series. He described her death
(lynched by a mob of Christians) as he strolled through the halls of the library of Alexandria, courtesy of the magic of video matting. Another machine was named Sofia. There are actually a number of historical astronomers named Sofia, but the machine in question was named in honor of Sofia Kovalevskaya. Sofia would probably never have thought of herself as an astronomer, but some of the mathematical work she did laid the foundation for understanding rotational and orbital dynamics, important considerations in astronomical problems.

On January 15, 1850, Sofia Krukovsky was born into a family of lesser Moscow aristocrats.
Typical for that social stratum, she was neglected by her parents and raised by a strict governess, who
instilled in Sofia the traditionally feminine traits of self-doubt and insecurity. The child was ignored to
the extent that the walls of her room were left bare of decoration, so the servants covered them with
cast-off old notes from her father’s calculus studies. For Sofia, this was a rare link to her father and family,
many of whom, it turned out, were mathematicians. When she was fourteen years old, she taught
herself trigonometry in order to understand a problem in an optics textbook. She corresponded with
the book’s author, Professor Tyrtov, who convinced her father to cultivate the impressive natural talent
that lurked in the unassuming young woman.

After a few years of private tutoring in St. Petersburg (as schools were not open to young
women), Sofia wished to attend university. The closest universities that admitted females were in
Germany, but there was another problem; they would only admit married women (single women
would have compromised the concentration of the male students). So, Sofia accepted a marriage of
convenience to Vladimir Kovalevsky. The marriage caused problems for Sofia, and throughout its fifteen
years it was a source of intermittent sorrow, exasperation and tension — her concentration was broken by frequent quarrels and misunderstandings with her husband. Sofia didn’t lack for money, however, so the young paleontologist and entrepreneur accompanied her to Heidelberg. Soon after, she decided to
move to Berlin to study under the famous mathematician Karl Weierstrass. Dr. Weierstrass didn’t know what to think of the young female student at first, but Sofia’s work won him over, and a true professional friendship was formed. She is quoted as having said, “all my work has been done precisely in the spirit of Weierstrass.” In four years she had produced three papers (on partial differential equations, Abelian integrals and Saturn's rings), each of which Weierstrass deemed worthy of a doctorate. 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.

Sofia was awarded a doctorate in 1874, but was unable to find work despite the impassioned recommendations of Weierstrass. She returned home to aging parents, and for some time dedicated herself
to domestic responsibilities. A daughter was born to her and Vladimir. Soon after, Sofia returned to
her work in mathematics with a renewed fervor. Gosta Mittag-Leffler, a former student of
Weierstrass’s invited her to lecture at the University of Stockholm. At first this was a temporary position,
but after five years of excellent teaching and spectacular publications, the university offered her
tenure. In 1885 she was offered the Chair of the mathematics department.

These years, while filled with professional triumph, were unfortunately marred by personal
tragedy. None of Vladimir’s business ventures had panned out, and in a fit of despair he had committed suicide in 1883. Vladimir and Sofia had been separated for two years, and after the initial shock, Kovalevskaya immersed herself in mathematical work in an attempt to rid herself of feelings of guilt. In cruel
succession, Sofia’s beloved sister Anya died in 1887. In 1888 she completed perhaps her most
important work, “On the Rotation of a Solid Body about a Fixed Point.” Prior to Sofia’s work, the only
solutions for the motion of a rigid body about a fixed involved cases where the body was symmetric.
In her paper, Sofia developed a description of an asymmetrical body’s rotation where the center of its
mass is not on an axis contained in the body. This work was done in isolation, as she was excluded by
her gender from any mathematical library and/or professional society. Nonetheless, the paper was
entered in a competition for the French Academy of Science’s Prix Bordin … and won. The paper was
so highly regarded, the prize money was increased from 3000 to 5000 francs.

Sofia had been plagued by depression and anxiety all her life, and a scandalous affair with an academic
colleague in Stockholm didn’t help matters. In 1890 her health began to fail, and in 1891, at the height of
her mathematical powers and reputation, Sofia died of pneumonia. She was honored in 1951 and
1996 with a series of postage stamps (see images), and has a lunar crater named after her as well. Throughout her life, Sofia had to constantly prove that she deserved consideration as a serious mathematician, and finally at the end it seemed that the academic community had accepted her. Her life was filled with the personal stresses imposed upon her by her social status, rigid upbringing, forced marriage, and unusual career choice. With so many weights on her mind and spirit, one wonders what else she might have produced had she had an easier path.

References for this article can be found at http://www.agnesscott.edu/lriddle/women/ kova.htm.

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