Sonya Kovalevsky was one of the greatest mathematicians of the 19th century, and is described as the greatest female mathematician since Hypatia of Alexandria in the 4th century. Sonya is best known for the Cauchy-Kovalevsky theorem which is integral to the field of partial differential equations. She was also a talented author and wrote the powerful novel “The Sisters Rajevski” which was based upon accounts of her own life, and is considered an accurate portrayal of the life of the Russian intelligentsia at the time.
Sonya was born on January 15th, 1850 in Moscow, Russia, and her family belonged to the privileged social elite. Her father was a military officer and landholder while her mother was an accomplished musician. However, being born in this situation limited her possibility for intellectual growth as it did for most women in the 1800s. Sonya learned science and mathematics at a very early age from her self-educated uncle; he taught her to play chess as well as techniques for squaring the circle and solving asymptotes.
When she was eleven years old, her room was temporarily decorated with some old calculus lecture notes from her father’s time at university. She recognized some of the concepts from her studies with her uncle, and spent hours examining these notes, which to her were unintelligible, yet which she found extremely fascinating. By the time she was thirteen, Sonya excelled in algebra and geometry. However, her father did not feel it was correct for women to learn these subjects so he stopped her mathematical instruction. Sonya did not conform easily, however, and she borrowed an algebra book from one of her tutors, continuing to study secretly by night.
By the time Sonya was fourteen, her family’s neighbour gave them a copy of an elementary physics textbook he had written, and it is while reading this that Sonya encountered trigonometry for the first time. In order to understand the trigonometric identities, Sonya substituted a chord for sine and everything worked for small angles. She had rediscovered the method for deriving the sine law. Her neighbour, the professor, was so impressed by Sonya’s ability that he tried to convince her father to arrange some serious mathematical training for her. After four years, her father agreed to allow Sonya to take courses in analytical geometry and calculus in St. Petersburg. She quickly mastered the concepts in one winter; it seems that she was quite familiar with much of the material, as it adorned the walls of her childhood bedroom.
In the nineteenth century, Russian universities were closed to women, and Sonya received difficult treatment from the academic community. While Swiss and German universities admitted some women, women were not permitted to go abroad alone, and thus Sonya found herself stranded in Russia. For this reason, Sonya married Vladimir Kovalevsky, a young palaeontologist, in order that she may be free to study mathematics and science at Heidelberg, a prestigious German university. However, there she was not permitted to attend lectures, but with the help of the academicians at Heidelberg she was sent to the most renowned mathematician in Germany at the time, Karl Weierstrass at the University of Berlin.
Women were not permitted to even attend lectures at the University of Berlin, and this barred Sonya from being able to advance her studies. She was, however, determined and approached Weierstrass seeking help. Weierstrass challenged her with several problems he had prepared for his brighter students, with the expectation that Ms. Kovalevsky would not return. To the surprise of Dr. Weierstrass, she completed a set of unique solutions to all of the problems he had assigned her. Weierstrass quickly became convinced that Sonya was the most promising and the brightest of his students. He then taught her privately, and shared not only his lecture notes, but also his unpublished work.
By 1874, Sonya had provided the mathematical world with three original works of her own, each one worthy of a Ph.D thesis of itself. The first was on the shape of Saturn’s rings, the second was on elliptical integrals, and the third was in the field of partial differential equations, leading to the famous Kovalevsky-Cauchy theorem. Since the University of Berlin would not issue Sonya a degree, Weierstrass presented these works to the University of Gottingen who awarded her a degree based solely on the merit of her papers, even though she had never attended the university.
Sonya was subsequently exhausted, and returned to St. Petersburg where she began writing as a theatre reviewer, and science and technology reporter for a St. Petersburg newspaper. She then began to work on her first novel. For six years, she did no mathematical work, and in its stead wrote fiction while giving birth to her first daughter. However, when bankruptcy arrived, the Kovalevsky family eventually fell apart, and after this heart-breaking loss, Vladimir committed suicide in 1883. Also in 1883, the University of Stockholm, under constant pressure from Gosta-Mittag Leffler, an ex-student of Weierstrass, offered Sonya a probationary position in the Mathematics department. She gave all of her lectures at Stockholm in Swedish, and became so popular with her students that the University offered her a five year position.
The climax of Sonya Kovalevsky’s career came in 1888 when she was awarded the Prix Bordin, a prestigious award given by the French Academy of Sciences, for her work on the problem of the rotation of a solid body around a fixed point. After winning this award, she was given a lifetime chair at the University of Stockholm and became the first woman ever elected to the Russian Academy of Sciences. However, the Academy did not allow her to participate in their meetings because she was a woman.
In the years from 1888 through 1891 she worked on two novels and wrote numerous newspaper articles, demonstrating her well-rounded talents. This period, however, was difficult for Sonya as she was separated from her daughter who was left behind in Russia, her sister was dying a painful death, and a three-year romantic relationship had ended. Sonya died in 1891 from pneumonia following epidemic influenza. Sonya Kovalevsky’s life was an ideal for those who want to leave their records in the annals of history, she lived a full life, and her efforts were later rewarded, as she became the first woman to be commemorated on a Russian postage stamp, and she has since had a crater on the moon named after her.
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