The right equation
Name: Sofia Kovalevskaya
Fields: Mathematics and mathematical physics
Claim to fame: Innovative theories on differential equations and the rotation of a rigid body
During her short life, Sofia Kovalevskaya (1850-1891) had a remarkable career in mathematics, despite the many personal tragedies she endured. Overcoming the prejudices of her age, she came up with groundbreaking mathematical theories and paved the way for future discoveries. She was the third woman in Europe to get a regular chair in mathematics.
The calculus on the wall
Sofia Vasilyavna Korvin-Krukovsky was the middle child of Vasily Korvin-Krukovsky, a general in the Russian army, and Velizaveta Shubert, who were both well-educated members of the nobility. Born in Moscow on 15 January 1850, Sofia was also sometimes known as Sonya and, in her professional life, used the masculine form of her husband’s surname to avoid revealing her gender in publications.
Attracted to mathematics at a young age, Sofia was educated by tutors and governesses at the family’s estate, Palabino, and later in St Petersburg. She was greatly influenced by her uncle, Pyotr Vasilievich Krokovsky, who had a keen interest in mathematics and often spoke to Sofia on the subject. At the age of 11, Sofia papered the walls of her room with pages of lecture notes on differential and integral analysis, which provided the young mathematician with an introduction to calculus.
From Russia with love
Upon finishing her schooling, Sofia’s ambition was to study mathematics at university. Knowing that this was impossible for a woman in Russia, she formulated a plan to travel to western Europe. As young, unmarried girls were not allowed to travel alone without permission from their father, Sofia entered a marriage of convenience with Vladimir Kovalevsky, then a young palaeontology student. In 1869, they left Russia and travelled to Heidelberg, Germany, where Sofia hoped to study mathematics and natural sciences. On arrival, she was informed that women were not allowed to enrol in courses, but she lobbied the university’s authorities who eventually permitted her to attend lectures and seminars in physics and mathematics.
In 1871, Sofia moved to Berlin where she studied privately with the great calculus expert Karl Weierstrass. By the spring of 1874, she had completed three papers, all of which Weierstrass considered worthy of a doctorate. Later that year, on Weierstrass’ initiative, the University of Göttingen awarded her (in her absence and therefore without a defence) a doctorate, summa cum laude, for her work on partial differential equations.
Sofia began to look for an academic post but was informed that the best she could do would be teaching arithmetic to schoolgirls. Returning to Russia, the situation was no better and, disillusioned, Sofia abandoned her mathematical work for six years. During this time, the marriage of Sofia and Vladimir turned into love, and they had a daughter, also called Sofia. Moreover, they became involved in various business ventures. When these schemes collapsed, in 1883, Vladimir committed suicide.
The lady professor
By the time of Vladimir’s death, Sofia had resumed her mathematical work on a private basis. She presented a paper on Abelian integrals at a scientific conference in 1880, which was very well received. In 1882, Sofia began to work on the refraction of light, writing three articles on the topic. The following year, she got the break she needed to get into the academic world when she received an invitation from a mathematician who had met her at the conference in 1880, Gösta Mittag-Leffler, to lecture at the University of Stockholm on a temporary basis. During her time in Sweden, Sofia taught courses on the latest topics in analysis and carried out important research. After fi ve years, she was appointed as a professor, making her the first woman since Laura Bassi and Maria Gaetana Agnesi, in the 18th century, to hold a chair at a European university.
The body mathematic
Whilst at the University of Stockholm, Sofia was appointed editor of a new journal, Acta Mathematica, and also became involved in the organisation of international conferences. Her greatest triumph came in 1888 when her paper ‘On the rotation of a solid body about a fi xed point’ won the prestigious Prix Bordin, organised by the French Academy of Sciences. So impressed was the Academy by the work that they increased the prize money from 3 000 to 5 000 francs. Her work was particularly innovative because existing solutions for the motion of a rigid body around a fi xed point had been developed for cases where the body is symmetric; Sofia’s paper developed a theory for an unsymmetrical body, where the centre of mass is not on an axis in the body.
In 1888 she began a ‘scandalous’ affair with Maxim Kovalevsky, the nephew of Vladimir, and in 1891 she travelled to Paris to meet him. Whilst there she contracted influenza, complicated by pneumonia, which led to her death on 10 February.
though her life was cut short, Sofia Kovalevskaya’s career was a remarkable one. Although she published only ten papers on mathematics and mathematical physics, many of these included ground- breaking
theories or the impetus for future discoveries. Her early work on the theory of differential equations was a particularly valuable contribution to mathematics and led to what is now known as the Cauchy-Kovalevsky theorem for analytic partial differential equations. Kovalevskaya’s other great breakthrough was her paper on the rotation of an unsymmetrical solid body around a fi xed point, now known as the Kovalevsky top. Her further research on the topic won her a prize from the Swedish Academy of Sciences in 1889. Sofia was able to overcome the general objections to women in science by demonstrating her intelligence and her groundbreaking work in mathematics. She was rewarded with a professorship and a role editing a mathematical journal. Perhaps her most lasting influence, however, was the example she set for other women trying to enter academia.