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A Convergence of Lives: Sofia Kovalevskaia : Scientist, Writer, Revolutionary

Ann Hibner Koblitz
Rutgers University Press
Publication Date: 
Number of Pages: 
Lives of Women in Science
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The Basic Library List Committee considers this book essential for undergraduate mathematics libraries.

[Reviewed by
William J. Satzer
, on

This biography of Sofia Kovalevskaia, first published in 1983, was reissued in 1993 by Rutgers University Press as a volume in a new series called Lives of Women in Science. The book is subtitled Sonia Kovalevskaia: Scientist, Writer, Revolutionary. Kovalevskaia (more commonly referred to now as Kowalevski) lived a rich and accomplished life as a mathematician and a writer and is surely the most well known woman in mathematics of the nineteenth century.

Kovalevskaia was born in Moscow in 1850 to a wealthy family. She grew up in a sheltered environment on a provincial estate. She was tutored in mathematics and showed considerable interest and talent. Russian universities were closed to women, so she contrived a marriage of convenience that allowed her a measure of independence that eventually allowed her to continue her study of mathematics in Germany. After attending lectures in mathematics and physics at Heidelberg she moved to Berlin to work with Weierstrass. She wrote three dissertations with him, the last including a proof of what we now call the Cauchy-Kowalevski theorem. Weierstrass’s influence was sufficient to persuade the powers at Göttingen to grant her a doctorate.

She and her husband moved back to Russia after both had completed their doctorates, but neither found employment. They had a daughter, got involved in the social, financial and political turmoil of the times and abandoned their academic pursuits for some time. After her husband committed suicide, Kovalevskaia’s widowhood provided the respectability she needed to approach European universities. Mittag-Leffler got her an appointment at the University of Stockholm and her career took off. She died at the age of 41.

The author is particularly good at portraying the social and cultural background of her subject, and especially the intellectual and political environment in Russia. Sofia Kovalevskaia was known by many of the leading figures of her day — writers, scientists and political figures. Both she and her sister Aniuta were close acquaintances of Dostoevskii. The breadth of her connections is absolutely amazing — Darwin, George Eliot, Grieg, Chekhov, Turgenev, and many others.

The mathematical portion of the biography is less satisfying. The author is not a mathematician, and she naturally relies on others’ opinions to evaluate Kovalevskaia’s scientific merit. But she does this uncritically, and the result is a stream of favorable reports and quotations that testify to Kovalevskaia’s genius. Perhaps the most exaggerated is: “At the time of her death Kovalevskaia was considered the equal of anyone of her generation. This included even Poincaré, Picard and Mittag-Leffler.”

Kovalevskaia’s work deserves to stand on its own merits, and has no need of such hyperbole. She published ten papers, of which the most significant are probably the proof of the Cauchy-Kowalevski theorem and her proof of integrability for a kind of rigid body motion that included the asymmetrical top. Her work on the latter was particularly ingenious. She faced a considerable number of obstacles and more than her share of detractors. It is worth noting that few of the many barriers she encountered came from mathematicians. In particular, Weierstrass, Mittag-Leffler, Hermite and Königsberger were all strong advocates and, when they needed to be, defenders.

This is a fascinating biography of a remarkable woman and well worth reading.

Bill Satzer ( was a senior intellectual property scientist at 3M Company. His training is in dynamical systems and particularly celestial mechanics; his current interests are broadly in applied mathematics and the teaching of mathematics.

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