Sofia Kovalevskaya (née Korbin-Kukóvskaya), born in 1850 in Moscow, is one of the great mathematicians in history. However, she is not so well known for her revolutionary and literary role, which she intensely developed in her short life. Few scientists will be able to include in her biographies having participated in the Paris Commune of 1871. In addition to this, Kovalevskaya intervened in the progressive political and feminist currents of Russian nihilism at the end of the 19th century and also wrote several non-mathematical works; among them, some memoirs, a russian childhoodtwo plays (in collaboration with Duchess Anne Charlotte Edgren-Leffler) and a partially autobiographical novel, a nihilist (1890). This last text was written a year before his death in Stockholm, where he had found refuge and work with the help of the mathematician Gosta Mittag-Leffler.
The novel begins when the narrator is 22 years old and moves to Saint Petersburg after her stay in a small university town in Germany, where she had gone to study mathematics. This fact coincides with Sofia’s return, in 1874, from Berlin, where she arrived after passing through Heidelberg, following the advice of Hermann von Helmholtz and Leo Königsberger. Since the University of Berlin did not admit women, the mathematician Karl Weierstrass He taught her privately.
Together with him he carried out his research on partial differential equations, proving what is now known as Cauchy–Kowalevski theorem. This is an exceptional result within the theory of differential equations. On the one hand, it is the only result on existence and uniqueness of solutions that applies to differential equations of any kind. On the other hand, however, it only works for a very specific and restrictive type of solution, called analytic, which limits the practical usefulness of the theorem. This and other results earned her her doctorate (under the supervision of Weierstrass) from the University of Göttingen, where a woman could get a doctorate; although, her thesis was judged in absentia since he was not allowed to take the oral exam.
After visiting England, he returned to Saint Petersburg and then to Moscow. In Russia, despite Weierstrass’s recommendations, he did not get any university employment, but he integrated himself into the literary circles of the city. In the book, it is in these intellectual circles of St. Petersburg that Vera appears, a descendant of an important family of the Russian agrarian nobility fallen on the decline. Vera is interested in the political ideas of the nihilists through her teacher and also her lover, arrested and imprisoned by the Tsar’s police for his liberal ideas.
According to Ann Hibner Koblitz in Science, Women and Revolution in Russia, “For the first nihilists, science was practically synonymous with truth, progress and radicalism; therefore, the pursuit of a scientific career was by no means considered an obstacle to social activism. In fact, it was seen as a positive impetus for progressive forces, an active blow against backwardness.”
This was surely the case with Sofía, although in the book she presents, through Vera, a less flattering image of mathematicians (and is the only mention of this discipline in the novel). “And as for Vera’s feelings towards me, she preferred me over everyone she knew, and at the same time I couldn’t understand why she gave me completely to mathematics. It seemed to him that a mathematician was someone like a rare being who was in charge of solving puzzles expressed in figures and who could be forgiven for his obsession because he was a very innocent being and at the same time it was difficult not to despise him for his weakness.
Precisely, in order to fully devote herself to her research career, Sofía had to move to Stockholm, where Mittag-Leffer obtained a permanent position for her at the university. In Sweden, Ella Sofía developed an intense work as a researcher, becoming editor of the prestigious journal Acta Mathematica. Among other discoveries, she described the movement of what is known as Kovalevskaya’s spinning top, a new example of a rigid body rotating in the presence of gravity, whose dynamics are integrable. His work improved, 100 years later, on the earlier models of Leonhard Euler and Joseph-Louis Lagrange. Sofia herself died in Stockholm, a victim of influenza complicated by pneumonia, on February 10, 1891.
Manuel de Leon is a research professor at Superior Council of Scientific Investigations at ICMAT.
Agate Timón García-Longoria is coordinator of the Mathematical Culture Unit of the ICMAT.
Coffee and Theorems is a section dedicated to mathematics and the environment in which it is created, coordinated by the Institute of Mathematical Sciences (ICMAT), in which researchers and members of the center describe the latest advances in this discipline, share meeting points between mathematics and other social and cultural expressions and remember those who marked their development and knew how to transform coffee into theorems. The name evokes the definition of the Hungarian mathematician Alfred Rényi: “A mathematician is a machine that transforms coffee into theorems”.
Edition and coordination: Agate A. Timón G Longoria (ICMAT).
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