Alexander Kleitman

The paper recounts the history of the first defense of doctoral dissertation in mathematics in Russia that occurred in 1837. The author of this dissertation devoted to partial differential equations was Nikolai Efimovich Zernov (1804–1862). By the time when he worked on his dissertation, an abundant material concerned with the methods for integrating some types of partial differential equations had been accumulated in Western Europe. This material, however, had not been systematized, which was not conducive to the development of the theory of partial differential equations as a separate area of mathematics. Having set himself a task to close this gap, Zernov accomplished it brilliantly.

Zernov's dissertation had a distinctive structure: the first chapter dealt with the integration of partial differential equations in closed form; the second chapter, with the forms of integrals (solutions) of these equations; and the third chapter, with the geometric theory of partial differential equations.

The paper reconstructs some facts from the scientist's biography for the first time and analyzes how the dissertation was defended. It is shown that, in his study, Zernov introduced a number of improvements and simplifications in partial differential equations integration methods proposed by his predecessors and set forth his results in a comprehensible form in the Russian language.

Zernov's work helped to raise the level of mathematical education in Russian universities, particularly in Moscow University. It was largely due to his dissertation that the theory of partial differential equations became one of the favorite fields of research for Moscow mathematicians (A. Yu. Davidov, V. V. Preobrazhenskii, D. F. Egorov).