Mathematician Profile# Sofya Kovalevskaya: Never Take No For An Answer

November 29, 2021

*By Lillie Therieau*

The fascinating life of Sofya Kovalevskaya is made even more extraordinary by the barriers she had to overcome as a woman in the maths and sciences in late 19th century Europe. Sofya was constantly told she could not enter academic spaces, earn advanced degrees, or exist on the same plane as her male colleagues. In each of these circumstances, she found a way around the sexist roadblocks, fighting her way to becoming the first woman to be awarded a doctorate.

Beyond her academic accomplishments and pioneering work, Sofya was also present for some of the most turbulent and impactful events of the late 19th century. Dive into Sofya’s world to be inspired by this truly courageous woman, who never took no for an answer!

Sofya Kovalevskaya was born in Moscow, Russia in 1850. Her father was a Lieutenant General in the Russian Imperial Army, and her mother’s family descended from a long line of scientists. Due to her family’s relative wealth, her parents were able to provide her with good-quality education from an early age. She had governesses that taught her several languages, as well as science and mathematics. In Sofya’s early studies, her teachers were stunned by her ability to figure out mathematical concepts on her own.

*Sofia Kovalevskaya (Image source: **Wikipedia**)*

Her physics tutor recommended that Sofya study with a notable tutor named Strannoliubskii, who could help foster her prodigal skills. Strannoliubskii was a well-known advocate of higher education for women, which was uncommon in Russia at the time. Sofya’s parents hired Strannoliubskii, who tutored her in calculus. When she completed her secondary education, it became clear that Sofya would need to leave Russia. She was enormously skilled in mathematics and science, but she could not study at institutions of Russian higher education due to her gender.

Sofya decided to study abroad, concocting a plan to get out of Russia. She would need a signed note from her father or husband to leave the country and attend school abroad, so she planned a fake wedding. Sofya married Vladimir Kovalevskij in 1868, a young radical and paleontology student who was only too happy to help Sofya achieve her educational dreams. The two moved to Germany in 1869 to pursue their respective academic goals.

After a lot of convincing, Sofya was allowed to audit classes at the University of Heidelberg. She studied under preeminent thinkers working in physics and mathematics, though she was not allowed to fully participate in the classes. In late 1869, Sofya and Vladimir visited London, where they spent time with thinkers like Charles Darwin, Thomas Huxley, and George Eliot. In fact, a conversation between Sofya and George Eliot is said to have influenced parts of the latter’s famous book, Middlemarch.

In 1870, Sofya moved to Berlin. However, no amount of convincing would allow her to audit classes at the university, so she befriended one of the professors, Karl Weierstrass. Weierstrass was so impressed by her ideas and work that he taught her all of the material that he covered in his classes at the university. In 1871, Sofya and Vladimir traveled to Paris to aid the Paris Commune. She helped treat those who were injured, which included one of her sisters. Overjoyed at their reunion, Sofya and her father later helped her sister and her husband escape execution after they were arrested when the Commune fell.

*Sofia with her daughter Sof’ya Vladimirovna in 1885. (Image source: **G. J. Tee, Math. Chronicle 5(1977) 113–139)*

Sofya returned to Berlin and continued to study with Weierstrass. In 1874, she presented three papers on mathematics and planetary physics as her doctoral dissertation. She earned her doctorate in mathematics and became the first woman to receive an equivalent degree.

In late 1874, Sofya and Vladimir returned to Russia, hoping that Vladimir would earn a professorship. He was denied a position for his radical views and the couple spent several years trying their hand at various money-making schemes, like real estate development, stock trading, and the oil industry. They had one child together, but after two years, Sofya left her daughter with relatives and friends and left Vladimir for good.

Sofya became a permanent professor at Stockholm University in 1889, becoming the first woman in Europe to hold the position. At the same time, she lobbied the Russian Academy of Sciences to admit her as a fellow. Finally succeeding, she became the first woman member of the Academy, though she was never granted a professorship in her home country. As a feminist and progressive thinker, Sofya put her thoughts down on paper towards the end of her life, writing a semi-autobiographical novel and plays, which often dealt with politics and feminist thought. Sofya died of influenza and pneumonia in 1891, which she contracted during an epidemic breakout. She was only 41 years old!

Sofya’s most notable mathematical contribution is the Cauchy-Kovalevskaya theorem. This theorem addresses partial differential equations, which are used to understand the way fundamental physical building blocks behave: such as liquids, heat, gravitational waves, and sound. Each of these physical building blocks sometimes moves or behaves in oscillatory patterns. Partial differential equations can model the exact ways that these movements will play themselves out.

*Oscillations*

The Cauchy-Kovalevskaya theorem proves that, when there are suitable initial conditions, partial differential equations have unique solutions. This was a critical development in the field of physics, as these equations are important for understanding the way the universe around us functions. While the Cauchy-Kovalevskaya theorem does not show how to solve these equations, it informs mathematicians and physicists under which conditions a solution can be found.

Knowing when a solution to partial differential equations exists is important because it allows researchers to discover many of the hidden properties of sound, heat, and other physical phenomena.

Sofya has been a role model for young mathematicians for centuries. She refused to take no for an answer, working twice as hard as her male counterparts to be allowed to speak in the same spaces. After her death, Sofya was widely recognized as a critical voice in late 19th-century mathematics. Today, Sofya Kovalevskaya has a lunar crater named in her memory. She’s been the star of numerous books, biographies, movies, and biopics.

This article is the sixth in our series exploring the lives and achievements of famous mathematicians throughout history. (Our last article was about the Iranian mathematician Maryam Mirzakhani!)

Through the lives of these brilliant folks, we hope you’ll find connections, inspiration, and empowerment.