Page:Russian Realities and Problems - ed. James Duff (1917).djvu/192

 of great practical value and inspired no alarm in the Government.

It is natural, therefore, that mathematics have continuously developed in Russia from the times of Bernoulli and Euler. The latter trained the first Russian mathematicians who were able to use mathematical analysis, particularly Kotelnikov and Rumovsky. Somewhat later Guryev demanded stricter method in mathematical investigations, and Ossipovsky tried to systematize mathematical knowledge; at the same time he bestowed his attention upon the rising genius of Ostrogradsky. After studying in Paris, especially under Cauchy, Ostrogradsky wrote some noteworthy papers, especially on the integration of algebraic functions and the calculus of variations. Together with Bunyakovsky, Ostrogradsky was one of the founders of the Russian mathematical school, which gained great distinction from the work of a famous mathematician of the second half of the century, Chebyshev, who discovered new solutions of many difficult mathematical problems. Chebyshev elucidated the theory of probabilities, elaborated a remarkable theory of numbers, wrote valuable papers on integral calculus and interpolation, continued fractions, and problems concerning maxima and minima, etc.; he started, moreover, new problems which were further investigated by his pupils. Markov, who studied also under the influence of Korkin, was particularly interested in the theory of probabilities and of algebraic numbers and continued fractions; Lyapunov, who gave himself up to the study of theoretical mechanics, guided the first steps of Steklov, and so on. This movement in