Sofia Kovalevskaya: Mathematician and Writer

By Ernest Davis

Mathematician with the Soul of a Poet: Poems and Plays of Sofia Kovalevskaya. Translated, edited, and introduced by Sandra DeLozier Coleman. Bohannon Hall Press, November 2021. 252 pages, $19.95.

Many people consider Sofia Kovalevskaya (1850-1891) the greatest female scientist before Marie Curie and the greatest female mathematician before Emmy Noether. She was the first woman to receive a doctorate in mathematics and become a full university professor (with the exception of a handful of predecessors in Italy a century earlier). She also made a number of important original contributions to mathematics. For example, the Cauchy-Kovalevskaya theorem establishes existence and uniqueness for a broad class of systems of partial differential equations (PDEs); Augustin-Louis Cauchy proved a special case in 1842 and Kovalevskaya proved the general case in 1875. Her discovery of the “Kovalevskaya top”—one of very few cases of three-dimensional rigid body motion with integrable equations—earned her the Prix Bordin from the French Academy of Sciences in 1888.

In 19th-century Europe—and especially in Russia—ambitious, gifted women faced enormous obstacles at every stage of their lives. Both Kovalevskaya’s father and governess refused to let her learn algebra. Instead, she taught herself in secret — in part from books and in part, incredibly, from her father’s old math class notes that were recycled as wallpaper in her bedroom. In order to escape her father’s rigid control and be allowed to enroll in a university, Kovalevskaya entered into a “fictitious marriage” with fellow student Vladimir Kovalevsky. She moved to Germany and, through great efforts, was able to take classes in math and physics at the University of Heidelberg. She wanted to study at the University of Berlin, but the school would not even permit her to audit classes. However, mathematician Karl Weierstrass met Kovalevskaya and was so enormously impressed with her talents that he tutored her privately. Weierstrass considered her to be the most talented of his many students and grew very attached to her; they remained lifelong friends.

In 1874, Kovalevskaya completed her thesis, which consisted of three papers: her aforementioned work on PDEs, a paper on the dynamics of Saturn’s rings, and a paper about elliptic integrals. Weierstrass successfully persuaded the University of Berlin to issue Kovalevskaya a doctorate even though she never attended classes or defended her thesis. For many years afterward, however, she was unable to obtain any kind of university position — no institution in Germany or Russia would consider such a thing. Finally, in part due to the efforts of Gösta Mittag-Leffler (who was also a student of Weierstrass), Kovalevskaya received an appointment as privat-docent at Stockholm University in 1883; she was later promoted to ordinary (full) professor in 1889.

Kovalevskaya led an altogether extraordinary life in her 41 years. She was a socialist, a feminist, and a radical. One illustrative instance occurred in early 1871 during the aftermath of the Franco-Prussian War. At the time, Paris was ruled by the Commune and under attack from the national army. Kovalevskaya and her husband traveled from Berlin and somehow smuggled themselves past the nearby German lines and into the besieged city to help her beloved elder sister, Anna, who was deeply involved with the Commune.

Kovalevskaya was also a gifted writer. Her best-known work, A Russian Childhood, is a personal memoir that is evocative, perceptive, moving, and extremely entertaining. Her account of novelist Fyodor Dostoevsky’s unsuccessful courtship of her sister Anna is a masterpiece of narrative and vivid characterization. While I have not read her semi-autobiographical novel, Nihilist Girl, it is said to be remarkable.

Translator Sandra DeLozier Coleman’s engagement with Kovalevskaya is itself a fascinating story that Coleman recounts in great detail. In addition to her 30-year career as a mathematics professor, Coleman is a poet, writer, and artist. In 1996, she served as a book reviews editor for AMATYC Review (a publication of the American Mathematical Association of Two-Year Colleges) and penned a review of three then-recent biographies of Kovalevskaya. Coleman became obsessed—the word is not too strong—with Kovalevskaya and avowed to translate her writings, despite the fact that she did not even know the Cyrillic alphabet at the time. In the 25 years since—and assisted by several Russian-speaking colleagues and friends—Coleman has pursued this goal with immense energy and dedication.

Her new book, Mathematician with the Soul of a Poet, is the fruit of these long labors. The text includes translations of nine of Kovalevskaya’s poems and a pair of plays that were not previously translated into English, along with extensive commentary and biographical analysis. It also contains a translation from German of a short poem by Weierstrass — a toast that he gave at his own 70th birthday party.

Kovalevskaya’s poems are a mixed bag. They are mostly written in rhyme and meter, though one is in free verse and another is a prose poem. Thematically, they include semi-humorous descriptions of her married life (one is even written from her husband’s point of view);¹ personal, introspective musings; and a strange fantasy of a young girl who daydreams about becoming a martyr. Coleman carries out the translations with extreme care to convey not only the meaning but also the meter, rhyme scheme, and music of the original works. Doing so is often very challenging. For instance, Kovalevskaya’s 32-line poem called “If You in Life” alternates between 12-syllable and 10-syllable lines and sticks to two rhymes in an ABAB scheme for its entire duration. The translation faithfully follows this overly constrained form.

Kovalevskaya’s two plays—How It Was and How It Might Have Been—are “parallel dramas” that form a pair called The Struggle for Happiness. They were written collaboratively by Kovalevskaya and her close friend Anne Charlotte Edgren-Leffler, who was an actress, writer, and sister of Mittag-Leffler. The two plays feature the same characters and opening situation, but the characters make different decisions at critical points that lead to opposite outcomes. How It Was is a tragedy that concludes with unhappy marriages, financial ruin, and a suicide, but How It Might Have Been has a happy ending in all respects. Coleman speculates that Kovalevskaya may have come to this idea through her interest in Henri Poincaré’s analysis of differential equations’ sensitivity to small changes in the initial conditions.

The book’s title, Mathematician with the Soul of a Poet, is derived from a passage in a letter by Kovalevskaya:

One of the foremost mathematicians of our century says very justly that it is impossible to be a mathematician without also being a poet in spirit. It goes without saying that to understand the truth of this statement, one must repudiate the old prejudice by which poets are supposed to fabricate what does not exist, and that imagination is the same as “making things up.” It seems to me that the poet must see what others do not see, must see more deeply than other people. And the mathematician must do the same.

Many researchers suppose that the mathematician she quotes was Weierstrass, and that Weierstrass was speaking not just of mathematicians in general but of Kovalevskaya specifically.

Judging by her literary works, I would say that Kovalevskaya had more the soul of a gifted writer of prose than the soul of a poet. I do not know why the former would be considered of lesser prestige. Moreover, she seems to have had an affinity for other great writers of prose; she remained a close friend of Dostoevsky until his death and visited George Eliot at her house a number of times — she even wrote an insightful reminiscence in tribute after Eliot’s passing. Yet whether poet or prosist, Kovalevskaya’s mind and soul were certainly extraordinary, and Coleman’s labor of love sheds a new and interesting light on the esteemed mathematician.

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¹ Kovalevskaya’s relationship with her husband was complicated. Their marriage was originally planned as a purely fictitious union so that Kovalevskaya could leave her father’s house, and she and her husband lived apart while she was a student. Later, however, they lived together and in fact had a daughter.

Ernest Davis is a professor of computer science at New York University’s Courant Institute of Mathematical Sciences.