# Sonya Kovalevsky

## Developer of Partial Differential Equations

Krukovsky was born in Moscow on January 15, 1850. When she was a young child, the family moved to a large country home. The family miscalculated the amount of wallpaper needed for Sonya’s bedroom and temporarily used pages from a mathematics lecture. These abstract diagrams and formulae fascinated the child. When she later studied the calculus at age 15, many concepts seemed familiar to her, to the astonishment of her tutor.

Because Russian universities did not accept female students at that time, Krukovsky sought ways to study abroad and promote her ideas about the emancipation of women. Her solution was a marriage of convenience to Vladimir Kovalevsky, who also wished to attend a university outside Russia. They were married in 1868 and, once established in Germany, the two went their separate ways. In Heidelberg, Kovalevsky quickly came to the attention of her professors because of her mathematical abilities. There she learned of the famous mathematician Karl Weierstrass who taught at the University of Berlin. Kovalevsky moved to Berlin, and, as that university did not enroll women, she became a private student of Weierstrass for the next four years. During this time she greatly expanded her understanding of differential equations. She also wrote three doctoral dissertations because she and Weierstrass believed that, as a woman, she would not be awarded a degree without extraordinary proof of her abilities. Her work on partial differential equations resulted in a doctorate in absentia (because women were denied residential study) from the University of Göttingen, summa cum laude, in 1874.

Neither her degree nor her outstanding recommendations were any help to her back in Russia. After several disheartening years in her homeland, Kovalevsky returned to Europe in 1884 to become a lecturer at the University of Stockholm. This was a time of intense creativity and work. She eventually was appointed a professor at the university, became a spokesperson for women’s rights groups in Sweden, and was an integral part of the intellectual community of Europe. In 1888 the French Academy of Sciences awarded Kovalevsky the Prix Bordin (an equivalent of the Nobel Prize) for her paper on how a rigid body revolves around a fixed point, its center of mass. Although others had studied this phenomenon in symmetric solids, Kovalevsky constructed an elegant explanation of the motion of asymmetrical crystals. Her work was deemed so strong that the prize amount was nearly doubled.

During the next few years Kovalevsky exhausted herself physically and emotionally. One of the things she accomplished was the publication of The Rajavski Sisters (1889), a novel based on her childhood. She eventually contracted pneumonia while traveling between Moscow and Stockholm. Her death in 1891 came at the peak of her career.

**Sonya Kovalevsky’s Legacy**

Kovalevsky not only broke new ground in mathematics and had an impact in nuclear physics, she also was influential in the women’s rights movement, particularly in education.

Kovalevsky’s credibility enabled other women to enter scientific and mathematical fields. As she gained the respect of the mathematics community, many academics acknowledged that a woman was capable of rigorous, intellectual work. During her time in Germany she helped several other young women gain entrance into previously male only research labs. Her nickname, “Princess of Science,” reflected her popularity and renown in Europe.

Kovalevsky’s work on infinite series had direct impact in nuclear physics; other implications of infinite series are still being explored. The foremost successor of Kovalevsky, LISE MEITNER, based some of her calculations of radioactive chain reactions on Kovalevsky’s work on infinite series. This made controlled nuclear fission possible—both for bombs and for electrical generation. A geometric series is one where the ratio of each term to its predecessor is as constant as the number of vibrations per second (the frequency) in the musical scale of a well tuned piano. But in an infinite series, the ratio gets repeatedly larger or smaller as when computing compound interest or declining balances in home mortgages, or in carrying out the value of pi to many decimal places. The limits and uses of infinite series have continued to interest mathematicians, scientists, and engineers since Kovalevsky’s time, as practical applications of this method of analysis continue to expand.

Sonya Kovalevsky – 18501891