VI.59 Sofya (Sonya) Kovalevskaya

b. Moscow, 1850; d. Stockholm, 1891
Partial differential equations; Abelian integrals

Kovalevskaya showed talent for mathematics at an early age but as a woman in mid-nineteenth-century Russia she was denied access to university. Unable to leave the country unescorted she married and in 1869 traveled to Heidelberg, where she was taught mathematics by Du Bois-Reymond. The following year she moved to Berlin to work with WEIERSTRASS [VI.44]. Berlin University was closed to women but Weierstrass agreed to tutor her privately. Under his supervision Kovalevskaya completed dissertations on partial differential equations (PDEs), Abelian integrals, and Saturn’s rings, and in 1874 she became the first woman to receive a doctorate in mathematics. The dissertation on PDEs, which excited particular attention, contained the result now known as the CAUCHY-KOVALEVSKAYA THEOREM [IV.12 §§2.2,2.4], an important tool in establishing the existence of analytic solutions of PDEs.

That same year Kovalevskaya returned to Russia and, unable to find a suitable position, temporarily abandoned mathematics. In 1880, at the invitation of CHEBYSHEV [VI.45], she gave a paper on Abelian integrals at a conference in Saint Petersburg. It was enthusiastically received and in 1881 she returned to Berlin. She saw Weierstrass frequently and devoted herself to the study of the propagation of light in a crystalline medium—a subject to which she had been led by studying the work of the French physicist Gabriel Lamé—and to the study of the rotation of a solid body about a fixed point. Later that year she moved to Paris to work with mathematicians there.

In 1883, championed by Mittag-Leffler, Kovalevskaya was appointed as a Privatdozent at the University of Stockholm. She also became an editor of Acta Mathematica, making her the first woman to join the board of a scientific journal. On behalf of Acta she liaised with mathematicians from Paris, Berlin, and Russia, providing an important link between Russian mathematicians and their western European counterparts. She continued to work on the rotation problem and in 1885 made the breakthrough that, three years later, would win her the prestigious Prix Bordin of the French Academy of Sciences. Prior to her work the problem had been completely solved for only two cases, both symmetrical. In the first, solved by EULER [VI.19], the center of gravity of the moving body coincides with the fixed point; and in the second, solved by LAGRANGE [VI.22], the center of gravity and the fixed point lie on the same axis. Kovalevskaya discovered that there was a third case, one that was asymmetrical and more complicated than the other two, which could also be solved completely. (It was later shown that there are no others.) The novelty of her results lay in her application of the recently developed theory of theta functions—the simplest elements from which ELLIPTIC FUNCTIONS [V.31] can be constructed—to solve Abelian integrals.

Kovalevskaya became a full professor of mathematics at the University of Stockholm in 1889, the first woman anywhere to achieve such a position. Shortly afterward, she was nominated by Chebyshev for corresponding membership of the Russian Academy of Sciences, her subsequent election breaking the gender barrier once again.

Further Reading

Cooke, R. 1984. The Mathematics of Sonya Kovalevskaya. New York: Springer.

Koblitz, A. H. 1983. A Convergence of Lives. Sofia Kovalevskaia: Scientist, Writer, Revolutionary. Boston, MA: Birkhäuser.