Sofya Kovalevskaya is arguably the most important female mathematician of the nineteenth century. Unfortunately, there wasn’t a lot of competition. And, sadly, Sofya died at the age of 41 of influenza. The common belief that mathematicians seldom do important work after the age of 40 isn’t really true – especially with respect to really creative mathematicians. (Paul Erdős was going strong almost up until his death at 83, Karl Weierstrass, Sofya’s most important mentor, was still teaching at a junior high school when he was 40; most of his seminal work in mathematical analysis was done after that.) So there’s no telling what Kovalevskya might have done if she hadn’t died so young.
Sofya’s memoir of her childhood begins with her earliest memories and concludes with a chapter on the friendship that developed between herself and her older sister Anna with Fyodor Dostoevsky. Sofya was only 15 at that time (1865), and Anna was 23. Dostoevsky seems to have had a romantic interest in Anna, but the younger sister was present at many of the encounters with Dostoevsky. The latter was about 44 at the time, had been a published author for almost 20 years, had just divorced his first wife, and was on the verge of publishing novels for which he is now best known.
Obviously, to have come to the attention of a man like Dostoevsky, Sofya and her sister weren’t from a family of “ordinary” people. Their father was a retired general of the Russian army and the owner of an impressive country estate. So the childhood of both Sofya and Anna was hardly a typical one. However, the estate was isolated and remote from important Russian cities like Petersburg. Although the children were supervised by several governesses and tutors, it doesn’t seem, based on Sofya’s memoir, that they were especially “spoiled” (except by comparison with children in much more impoverished circumstances).
The basic details of Sofya’s life are laid out in a 40-page introduction by the translator, Beatrice Stillman. Sofya herself has nothing to say in the memoir about her early interest in mathematics, let alone the details of her later accomplishments. The introduction doesn’t really say much about the mathematics either. We do learn that “At thirteen Sofya began to exhibit an aptitude and avidity for algebra.” Since access to higher education was completely unavailable to women in 1870’s Russia (or most other countries), Sofya’s burgeoning interest in advanced math was first noticed when she was in Heidelberg with Anna. After “enormous effort” Sofya managed to gain permission to attend lectures (but certainly not to enroll as a regular student).
Yet it was enough that Sofya’s mathematical abilities quickly came to the attention of her teachers. According to Stillman, “Sofya had come to a momentous decision for herself: that her true vocation was mathematics and that there was one mathematician in the entire world she wanted to study with – Professor Karl Weierstrass, of the University of Berlin.” Sofya certainly wasn’t daunted by eminent men – Weierstrass has a position in the history of mathematics comparable to that of Dostoevsky in the history of literature. Weierstrass did take her under his wing, and wasted little time ensuring that she received the mathematical education she deserved.
For readers interested primarily in mathematics, it must be understood that Kovalevskaya’s memoir is entirely about her childhood, up to the age of 15 – and only about scattered incidents at that. Don’t pick it up expecting to learn much about mathematical prodigies. Even so, it has interesting and charming stories. There is in the present volume, quite separate from the memoir, a 15-page “Autobiographical Sketch” that Sofya wrote in 1890. There are some nice tidbits in there, such as “In the field of mathematics in general, it is mostly by reading the works of other scholars that one comes upon ideas for one’s independent research.”
There is, also, a 20-page appendix “On the Scientific Work of Sofya Kovalevsky” by a (modern) Russian mathematician. Its focus is, first, on the “Cauchy-Kovalevsky Theorem”, which deals with partial differential equations. Sofya’s far-reaching generalization of Cauchy’s work was presented by Weierstrass in 1874 as Sofya’s PhD thesis. Secondly, Sofya’s comprehensive solution of a problem concerning “the motion of a heavy rigid body near a fixed point is described. This is an important result in classical mechanics.
Anybody seriously interested in the history of mathematics should find the present volume a very worthwhile read.