ThatsMaths

A brilliant Russian mathematician, Sonya Kovalevskaya, is the topic of the That’s Maths column this week (click Irish Times: TM029 and search for “thatsmaths”).

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

Sonya was born in Moscow in 1850, into an aristocratic and intellectually gifted family. When their house at Palibino was redecorated there was insufficient wallpaper, and the nursery walls were covered with lithographed lecture notes on calculus that her father had retained from his student days. Sonya 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 Sonya. Moreover, it was difficult for a single woman to travel unescorted. So, when she was just eighteen, a marriage of convenience was arranged with a young palaeontologist, Vladimir Kovalevsky. The following year, the couple travelled to Heidelberg, where Sonya obtained permission to attend lectures at the university.

In 1870 Sonya moved to Berlin. Regulations there prohibited her from auditing lectures but she received private tuition from the great mathematician Karl Weierstrass. He was enormously impressed by her dazzling intelligence. The professor, who was fifty-five and unmarried, was also smitten by the luminescent vivacity of the 20-year old Sonya, and they developed a warm personal relationship.

Under the supervision of Weierstrass, Sonya 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 the Frenchman Augustin Cauchy, is known today as the Cauchy-Kovalevskaya Theorem.

Sonya and Vladimir agreed that the 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.

At that time, European universities were at last beginning to open their doors to women. Sonya obtained a temporary lectureship in Stockholm, and 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 problems in dynamics that can be completely solved. The judges were so impressed that they increased the prize from 3000 to 5000 francs.

Sonya’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 a scientific journal.

But her career was to be cut short: shocked by her husband’s suicide, she was shattered by the early and sudden death of her sister Aniuta. She  became ill with pneumonia and died, aged just forty-one, in 1891.

Sonya Kovalevskaya’s mathematical work is of enduring value. She was the first woman to be awarded a PhD 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 the access of women to the academic arena.