The great innovators of the past: Sofia Kovalevskaya

Portraits: the great innovators of the past

The | Edge pays homage to the stories of great historical figures, men and women from the past, pioneers and pioneering innovators, who through the dissemination of their knowledge and discoveries in science and technology, helped revolutionise humanity.

Sofia Kovalevskaya, the ‘revolutionary’ mathematician

Sofia Vasilyevna Kovalevskaya

(Moscow, 1850 – Stockholm, 1891)

The second daughter of three children from a Russian family of minor nobility, Sofia Vasilyevna Kovalevskaya – known to many as Sonya – was the first woman to earn a doctorate in mathematics and become a professor at Stockholm University. However, her important achievements in mathematical analysis (fundamental contributions such as partial derivative equations) and mathematical physics (in particular, rational and celestial mechanics) were also the result of a much sought-after female emancipation.

Born to General Vasily Vasil evič Korvin-Krukovsky and Elisaveta Fedorovna Schubert, Sofia inherited talent from her ancestors: her grandfather was a famous mathematician and her great-grandfather had been a famous astronomer.

As a child, she suffered from an aloof relationship with her parents, believing that they paid little attention to her. Growing up with her governess, the English Miss Smith, the child spent a lot of time reading books and composing (hidden from everyone) poems. Her only entertainment was chatting in the country house with her uncle Pjotr, who somehow steered her towards a bright future.

Although not fully grasping the meaning of the mathematical demonstrations and concepts enunciated by her uncle (among them, the ‘squaring of the circle’), Sofia became curious about this mysterious subject.

In her autobiographical book, Memoirs of Childhood, she recounts the anecdote of hours spent gazing at the walls of her bedroom, trying to understand a passage or sequence from the differential calculus of Prof. Ostrogradskj (the father of probability theory), papered on the wallpaper.

With a private tutor, at the age of eight, she began to study arithmetic systematically but, in reality, Sofia is (and will remain) fascinated by the more abstract and philosophical aspects of mathematics, such as the concept of ‘infinity’. To take private lessons in mathematical analysis, she goes to St Petersburg. But the young girl’s father has other plans for her and her older sister Anjuta, namely to find a good match to marry them off.

In the Russia of the time, university remained closed to women but Sofia did not resign. The only way was expatriation but, to do so, it was necessary to be on her father’s or husband’s passport: in short, you had to be married. Sofia accepted Vladimir Onufievic Kovalevsky, a Russian palaeontologist and early follower of Charles Darwin, as her ‘husband’. He agreed to a ‘fictitious marriage’: the union was celebrated in September 1868, as soon as the girl came of age.

Soon after, the two set off for Heidelberg, where Sofia was able to attend courses by the university’s most accredited lecturers: physicists Gustav Kirchhoff and Hermann von Helmholtz, chemist Robert Bunsen.

Then, they move to Berlin where the young woman can follow the most influential mathematician of the time: Karl Theodor Weierstrass. Curiously, the German university does not admit women in the classroom and a new challenge opens up for Sofia: convincing him to give her private lessons. The professor is not a feminist champion but is surprised by the references of his colleagues in Heidelberg and Sofia’s ingenious solutions to some mathematical exercises. So, he accepts her as his pupil: it is the beginning of a marriage of personal friendship and scientific research destined to last a lifetime (and to arouse a lot of envy in the environment).

During her years in Berlin, under the guidance of Weierstrass, she completed three dissertations – two on pure mathematics and one on astronomy – and edited a fourth. Her work is so good that it earns her a doctorate in mathematics from the University of Göttingen – the first time a woman has won this title. The publication of the results excited the scientific community (one of the theorems, that of Cauchy-Kovalevsky, is still cited).

Even in her private life at this time, her ‘revolutionary’ spirit emerges: at the time of the Commune, Sofia travelled to Paris to reunite with her older sister Anjuta, who was engaged in the struggle alongside fellow communist Victor Jaclard.

After Sofia’s graduation in 1875, the couple returned to St. Petersburg. But here no one recognises her achievements. For the scholar, it is a rude awakening: she rejects the offer to teach elementary arithmetic and is confined to domestic life. She falls back on helping her husband in various activities, which, however, go badly. Her only ‘consolation’ is attending a conference where she meets the Swedish mathematician Gosta Mittag-Leffler, also a child of the Weierstrass school: an acquaintance that will prove decisive.

After ten years of ‘fictitious’ union with Kovalevsky, in 1878, the two celebrated an official wedding and a daughter, Sofia, was born. But already during her pregnancy, the scientist reconnects with Weierstrass and her true ‘passion’: she starts working on mathematical problems again, both theoretical and applied. Russia and her role are tight for her, her husband’s business is in ruins, their relationship is on the rocks. Friends scramble to find her a suitable position.

In 1883, while in the French capital, she received news of her husband’s suicide. Absurdly, it became easier for Stockholm University to give a widow the official professorship in 1884.

These are the years of maturity, still full of success. Sofia works on the motion of solids under particular conditions (still known as the ‘Kovalevskaya case’), i.e. on the theory of the rotation of a rigid body around a fixed point (the motion of the spinning top). A problem of applied physics that has been studied since the 1700s, apparently simple but complex, which the scientist tackles by applying abstract results of pure mathematical theories. Her contribution was so decisive that in 1888 she was awarded the ‘prix Bordin’ (the Nobel Prize of the time).

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