al (in various senses of the word) control of physical or mechanical systems, which are described by differential equations, have led to the creation of the mathematical theory of optimal control. The related problems of the control of objects in conflict situations have resulted in the creation and development of the theory of differential games.
Studies in control theory and in related fields, combined with the progress in computing technology, have provided the foundations for automating new spheres of human activity.
Soviet mathematics holds a leading place in world mathematical science. The works of Soviet scientists play a decisive role in many fields. The advances of prerevolutionary Russian mathematics were connected with the work of outstanding individuals and encompassed a narrow range of topics. There were scientific mathematical centers in only a few cities (St. Petersburg, Moscow, Kazan, Kharkov, Kiev). The main achievements were associated with the work of the St. Petersburg school. After the Great October Socialist Revolution a number of important new directions were followed in the Moscow mathematical school. Such universities as St. Petersburg, Moscow, and Kazan were the main centers of mathematical research in prerevolutionary Russia. Since 1917 the development of mathematical research and applied mathematics has been closely linked with the development and growth of the Academy of Sciences of the USSR. Studies in mathematics are largely concentrated in the institutes of mathematics of the Academy of Sciences of the USSR, the academies of sciences of the Union republics, and leading universities. During the Soviet era the rise of many scientific schools in cities where previously no significant work was done in mathematics has been an important feature of the mathematical development in the Soviet Union. Such are the mathematical schools in Tbilisi, Yerevan, Baku, Vilnius, Tashkent, Minsk, Sverdlovsk, and other cities and the scientific school that was created in the 1960’s at Akademgorodok, near Novosibirsk.
Mathematical investigations are conducted abroad both in institutes of mathematics and at universities (especially in capitalist countries).
The first mathematical societies, which now exist in many countries, appeared as early as the turn of the 18th century. Extensive reports on world achievements in mathematics and its applications, as well as communications on the most interesting works of individual scientists, are read and discussed at the international congresses of mathematicians, held every four years (since 1898). The organization and encouragement of international cooperation in mathematics, the preparation of scientific programs for the international congresses of mathematicians, and other functions are tasks of the International Mathematical Union. Articles about current mathematical investigations, as well as news about mathematical events in various countries, are published in mathematical journals, which now total more than 250 (as of the early 1970’s).
REFERENCESPhilosophy and history of mathematics
Kolmogorov, A. N. “Matematika.” In Bol’shaia Sovetskaia entsiklopediia, 2nd ed., vol. 26. Moscow, 1954.
Matematika, ee soderzhanie, melody i znachenie, vols. 1-3. Moscow, 1956.
Zeuthen, H. Istoriia matematiki v drevnosti i v srednie veka, 2nd ed.
Moscow-Leningrad, 1938. (Translated from French.)
Zeuthen, H. G. Istoriia matematiki v XVI i XVII vekakh, 2nd ed. Moscow-Leningrad, 1938. (Translated from German.)
Van der Waerden, B. L. Probuzhdaiushchaiasia nauka. Matematika Drevnego Egipta, Vavilona, Gretsii. Moscow, 1959. (Translated from Dutch.)
Kol’man, E. Istoriia matematiki v drevnosti. Moscow, 1961.
Iushkevich, A. P. Istoriia matematiki v srednie veka. Moscow, 1961.
Wileitner, H. Istoriia matematiki ot Dekarta do serediny XIX stoletiia, 2nd ed. Moscow, 1966. (Translated from German.)
Wileitner, H. Khrestomatiia po istorii matematiki, sostavlennaia po pervoistochnikam …, 2nd ed. Moscow-Leningrad, 1935. (Translated from German.)
Klein, F. Lektsii o razvitii matematiki v XIX stoletii, par