The Woman Who Knew Infinity

In the nineteenth century, it was extremely difficult for a woman to achieve distinction in the academic sphere, and virtually impossible in mathematics. But a few brilliant women overcame all the obstacles and prejudice to reach the very top. The most notable of these was a remarkable Russian Sofia Krukovskaya.

Sofia was born in Moscow in 1850 into an aristocratic and intellectually gifted family. When her house at Palibino was redecorated, there was insufficient wallpaper, and they covered nursery walls with lithographed lecture notes on calculus that her father had retained from his student days. Sofia recalled reading these mathematical hieroglyphics with interest and wonderment, and they provided inspiration and impetus for her later career.

There was no opportunity for academic advancement in Russia for Sofia. It was difficult for a single woman to travel unescorted. So, when she was eighteen, they arranged a marriage of convenience, with a young paleontologist, Vladimir Kovalsky. The following year, the couple traveled to Heidelberg, where Sofia obtained permission to attend lectures at the university.

In 1870 Sofia moved to Berlin. Regulations there prohibited her from auditing lectures then she received private tuition from the brilliant mathematician Karl Weierstrass. Her dazzling intelligence enormously impressed him. The professor fifty-five and unmarried was also smitten by the luminescent vivacity of the twenty-year-old Sofia, and they developed a warm personal relationship.

Under the supervision of Weierstrass, Sofia began research on partial differential equations and in 1874. She was awarded a doctoral degree summa cum laude by Göttingen University. Her work, which extended that of Frenchman Augustin-Louis Cauchy, is known today as Couchy-Kovalevsky Theorem.

Sofia and Vladimir agreed that their nominal marriage could become a genuine one, and the couple returned to St Petersburg, where they had a daughter in 1878. But opportunities in Russia were few and, when Vladimir’s business affairs went awry, he took his own life.

European Universities were at last open their doors to women. Sofia received a temporary lectureship in Stockholm, where she earned a reputation as a superlative teacher. She won the prestigious Prix Bordin of the French Academy of Science for her research. The problem she solved is described in advanced mechanics texts as the Kovalevskaya top. An asymmetric gyroscope, one of the very few complexities in dynamics that can be unraveled. The judges were so impressed that they increased the prize from 3000 to 5000 francs.

Sofia’s brilliant research secured her a professorship in Stockholm, She was elected a corresponding member of the Russian Academy of Sciences, smashing another gender barrier. She also became an editor of Acta Mathematica, the first woman on the board of the scientific journal. But her career was to be cut short. Already shocked by her husband’s suicide, it shattered her by the early and sudden death of her sister Anuita. Sofia became ill with pneumonia and died, aged 41 in 1891.

Sofia Kovalevskaya's mathematical work is of enduring value. She was the first woman to be awarded a Ph.D. in mathematics and the first female professor of mathematics. She was a leader in the movement for the emancipation of women and did much to improve Women’s access to the academic arena.