In 1874, the University of Göttingen (Germany) awarded the title of doctor to Sofia Kovalevskaya. He was 24 years old. His thesis consisted of three parts, each of which would have sufficed to defend an "ordinary" thesis (that is, the thesis of a man). One of them was about the shape of Saturn's rings. The most important, the one that had really impressed his professor, enunciated and demonstrated an important general property on the solutions of a partial derivative equation: Cauchy-Kovalesvskaya theorem, as it is known today.
Although he read the thesis in Göttingen, Kovalevskaya had studied in Heidelberg and especially in Berlin, where the university was so reactionary that it did not allow women to even put their feet in their buildings. Your teacher, Karl Weierstrass, one of the founders of the modern mathematical analysis, he had to repeat in his own house the classes that he gave in the university.
To get this far, Kovalevskaya had shown great determination: to leave his native Russia, where women could not pursue higher education, and study mathematics in Germany had had to find a young man willing to contract with her a "white" marriage. He would find it in Vladimir Kovalevski, a biologist passionate about fossils and Darwin's translator into Russian, whom he married at the age of 19. They moved to Heidelberg in 1869. Sofia's sister also traveled with them - a husband was then enough to take care of two ladies - but he continued on his way to Paris to fulfill his destiny. Sofia and Vladmir visited it in 1871 and lived for a few weeks the Paris Commune, a "revolutionary" parenthesis in their studies.
When both had read their theses they returned to Russia, where none could find a job at the height of their training. They lived several unhappy years, in which they abandoned their scientific activity, had a daughter and lost a lot of money. Then Kovalevskaya decided to go back to mathematics and leave her husband. He was in Paris when he learned of his suicide in Moscow.
We have trouble understanding her today, but it was precisely her condition as a widow that made her colleagues worry about helping her find a job. GöstaMittag-Leffler, a Swedish mathematician, also a former student of Weierstrass, got the newly created University of Stockholm to hire her. He moved to Sweden in 1883 and began a new life: that of a professional mathematician, with classes, trips and congresses, committee and committee meetings, and above all, dedicated to research.
I had been thinking about a classic mechanical problem for a while: describing the movement of a solid fixed by a point. It was a difficult issue, in which there had been no progress since the contributions of such prestigious mathematicians as Euler and Lagrange in the eighteenth century. However, Kovalevskaya had a brilliant idea to solve it. His work, which today is known as the "Kovalevskaya top", Earned him an award from the Academy of Sciences of Paris, which he collected at the end of 1889.
Kovalevskaya enjoyed great recognition from the mathematicians of his time: in Germany, in France, in Sweden, but also in Italy and even, late, in Russia. His theorem on partial differential equations remains one of the basic results in this area of mathematics, and his spinning top has inspired beautiful works of algebraic geometry in the late twentieth century. His mathematical heritage is important despite his not very long life.
In effect, as a true heroine of the nineteenth century, she died of pneumonia at age 41. He still had many ideas, and not only mathematics, also literary; years before he had written some Memories of youth and the novel A nihilist. It is said that his last words, on February 10, 1891, were "Too much happiness". Canadian writer Alice Munro made them the title of the beautiful story that he dedicated
Michéle Audin is a researcher at the University of Strasbourg and writer
Translation of Javier Fresán
Coffee and Theorems is a section dedicated to mathematics and the environment in which they are 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 points of contact between the mathematics and other social and cultural expressions and remind 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".
Editing and coordination:Agate Rudder (ICMAT).