Who was Sofya Kovalevskaya?

Some people, like Daniel Bernoulli, seem destined for a life of mathematics. Bernoulli, for example, was born to a wealthy family of mathematicians, and had easy access to the finest mathematics institutions in the world. Some people, however, became renowned mathematicians against the odds. Sofya Kovalevskaya was a mathematician who became well known for her work around the world, despite facing an uphill battle to study mathematics!

The Life of a Mathematician

Kovalevskaya was born in 1850 in Moscow. Her first exposure to mathematics came at a young age. Instead of using wallpaper, her parents covered the walls of her bedroom with sheets of calculus problems, which she said spurred an early interest in mathematics. However, after her childhood, paths to mathematics for women weren't easy - at the time, women were forbidden from attending universities in Russia, and the universities that accepted women were thousands of miles away. However, a friend of Sofia, a man named Vladimir Kovalevskij, pretended to be her husband so she could travel to Germany and study mathematics. 

Studying with Karl Weierstrass, a mathematician whose specialization was calculus, Sofia was able to graduate from the University of Heidelberg in 1874. However, owing to the discrimination against women at the time, she was barred from teaching at a university, despite being a doctor of mathematics. Thus, she spent the next few years away from mathematics, writing literature and helping Vladimir, who she decided to actually marry, with his business ventures. However, when Vladimir died, Sofia took up mathematics again.

In 1880, she wrote a paper on Abelian integrals that was well received. Following this, she wrote three papers on the refraction of light. This led to her appointment as a temporary professor at the University of Stockholm. Five years later, in 1889, she was granted the title of full professor, the first woman to earn the title in the 19th century at a European university (two women had been professors in the previous century). However, her life was cut tragically short, as she died two years later at the age of 41.

Kovalevskaya's Accomplishments

In addition to being a pioneer for women in the field of mathematics, Kovalevskaya made several important contributions to mathematics, many of which are still being studied today! Though she only wrote a few papers on mathematics, they contained several groundbreaking discoveries.

Her graduate school work on partial differential equations led to the creation of the Cauchy-Kovalevskaya Theorem. This theorem described a set of solutions for a set of differential equations.

Arguably Kovalevskaya's most notable contribution to mathematics was the idea of a Kovalevskaya Top. The 'top' isn't something that can be spun on a table, but rather deals with mathematical questions about rotation. Previously, Euler and Lagrange had studied the motion of rotating objects. However, Euler had only examined objects based on the center of gravity, while Lagrange had only looked at symmetrical objects. Kovalevskaya examined objects that weren't symmetrical, which led to the idea of the Kovalevskaya Top! This discovery won Kovalevskaya the Prix Bordin from the French Academy of Science, one of the world's most prestigious institutions at the time!