Sofya Kovalevskaya (1850-1891)

Russian mathematician and one of the first women to become a professor of mathematics

Affiliation: Heidelberg University (Germany), Stockholm University (Sweden)

“I began to feel an attraction for my mathematics so intense that I started to neglect my other studies.”

Sofya Kovalevskaya is one of the most successful and important mathematicians of all time. In addition to excellent research and significant contributions to the theory of partial differential equations and the mechanics of rotating rigid bodies, she was the first woman to receive a PhD in mathematics, the first woman to be appointed to a full professorship in Northern Europe, and the first woman to become editor of a scientific journal.

The greatest woman scientist before the twentieth century

Sofya Kovalevskaya was a Russian mathematician who made significant contributions to analysis, partial differential equations, and mechanics. However, she was also a groundbreaking advocate for women's rights and education and a pioneer for women in mathematics. At her time, women were not allowed to study at the university and, least of all, study mathematics. However, with a lot of patience and persistence, Sofya Kovalevskaya received a PhD in mathematics and later became a mathematics professor at Stockholm University after many years of struggle. She was also the first female editor of a scientific journal, Acta Mathematica. 

According to historian Ann Hibener Koblitz, Sofya Kovalevskaya was the greatest known woman scientist before the twentieth century.

The Cauchy-Kovalevskaya theorem

One of Sofya Kovalevskaya's most significant research achievements is the well-known Cauchy-Kovalevskaya theorem. Exceptionally talented in mathematics, she presented information on what would later become the Cauchy-Kovalevskaya theorem already in her PhD thesis.

The theorem is a cornerstone in the theory of partial differential equations (PDEs), particularly for understanding the behavior of solutions to initial value problems involving analytic functions. Its reliance on the analyticity of the data and the functions involved underscores the importance of this property in ensuring the existence and uniqueness of solutions to certain classes of PDEs. Augustin Cauchy proved a special case, and Sofya Kovalevskaya provided the full result.

The Kovalevskaya top

Another of Sofya Kovalevskaya’s original discoveries is the so-called Kovalevskaya top. This problem deals with a rigid body rotating around a fixed point. It is a classic example of a rigid body dynamics problem that is exactly solvable. Before her work, the problem had been completely solved for only two symmetrical cases. In the first, solved by Leonhard Euler, the center of gravity of the moving body coincides with the fixed point, and in the second, solved by Joseph-Louise Lagrange, the center of gravity and the fixed point lie on the same axis. Sofya Kovalevskaya discovered a third case, asymmetrical and more complicated than the other two, which could also be solved completely (it was later shown that there were no others). To this day, it remains an important example in classical mechanics and the theory of integrable systems.

Background and life

Sofya Kovalevskaya, also known as Sonya or Sofia Vasilyevna Kovalevskaya, was born in Moscow in 1850. She was the second of three children. Her parents were well-educated members of the Russian nobility, her father being an artillery general. She developed an interest in mathematics at a young age, influenced by her uncle, who introduced her to advanced mathematical concepts. At eleven, she accidentally got wallpaper in her room with differential and integrated analysis, further stimulating her interest in mathematics. Her parents nurtured her interest and hired a tutor who was a well-known advocate for higher education for women.

Despite her obvious talent for mathematics, Sofya Kovalevskaya could not complete her education in Russia since women were not allowed to attend universities. To study abroad, she needed written permission from her father or husband. Unable to leave the country unescorted, she married Vladimir Kovalevskij, a young paleontologist who later became famous for his collaboration with Darwin.

The first woman to receive a doctorate in mathematics

Sofya Kovalevskaya and Vladimir Kovalevskij emigrated from Russia in 1867. In 1869, Sofya Kovalevskaya began attending the University of Heidelberg in Germany, where she was allowed to audit classes as long as the professors approved. The following year, she moved to Berlin. Berlin University was closed to women, but Karl Weierstrass, a famous German mathematician often called “the father of modern analysis,” agreed to tutor her privately. Under his supervision, Sofya Kovalevskaya completed several papers, one of which was her groundbreaking work on partial differential equations, including the Cauchy-Kovalevskaya theorem. The other papers contained Abelian integrals and Saturn’s rings. In 1874, she became the first woman to receive a doctorate in mathematics after Karl Weierstrass had succeeded in exempting her from the usual required lectures and examinations.

That same year, Sofya Kovalevskaya returned to Russia. Despite her achievements, Kovalevskaya faced significant obstacles in finding an academic position in Russia due to her gender. She was faced with financial difficulties as well as personal challenges due to her husband's severe mood swings and uneven temperament. For some time, she worked as an assistant in her husband’s house-building business and helped neighbors electrify street lights.

Becoming a professor at Stockholm University

In 1881, she returned to Berlin, and later that year, she traveled to Paris, working with several prominent mathematicians. In 1883, championed by Gösta Mittag-Leffler, a Swedish mathematician, Sofya Kovalevskaya secured a position at Stockholm University. She also became editor of Acta Mathematica, making her the first woman to join the board of a scientific journal. In 1885, she made the breakthrough on the rotation problem that would win her the prestigious Prix Bordin of the French Academy of Sciences three years later. In 1889, she became a full professor of mathematics at Stockholm University, becoming the first woman to achieve such a position. Shortly afterward, she was nominated to join the Russian Academy of Sciences but was never offered a professorship in Russia. 

Sofya Kovalevskaya and Vladimir Kovalevskij had one daughter. After her birth, Sofya Kovalevskaya quickly returned to mathematics, leaving her daughter under the care of her sister. In 1883, Vladimir Kovalevskij committed suicide. In 1891, at 41, Sofya Kovalevskaya died of influenza complicated by pneumonia.