This article investigates the prevalent attitudes toward foreign influences and methodologies in Russian mathematics education at different periods in Russian history. The words "universal responsiveness" belong to Dostoevsky, who, in his famous speech on Pushkin, used them to characterize Pushkin's openness to the genius of all other nations. Moreover, Dostoevsky considered universal responsiveness to be typical of Russians in general. However, the isolationist tradition in Russia has been no less influential. At times this tradition has prevailed, at times it has retreated. It has expressed itself openly in political life--Stalin's campaign against "cosmopolites" was an especially striking example--and its impact on the development of literature and science has been the object of extensive research. Mathematics education, however, has rarely been looked at from this perspective. This paper will focus on a few select episodes from the history of mathematics education in Russia. These episodes, however, clearly demonstrate that a conflict between the isolationist and the internationalist traditions has taken place in this field as well. The paper contains a discussion of Leo Tolstoy's article "On the People's Education", little-known in the West, in which Russian mathematics education is aggressively and favorably contrasted with German methodologies. It also examines a methodological work from 1951, which includes a chapter entitled "From the History of the Struggle against Foreign Influences in Russian Mathematics." On the other hand, the article also looks at materials from Russian mathematics teachers' congresses from before the Russian Revolution, which illustrate Russian involvement and participation in processes taking place abroad. It also analyzes correspondence between the well-known Russian and American mathematics educators Dmitriy Sintsov and David Eugene Smith, discovered by the author, which facilitates a deeper understanding of certain aspects of the issues under investigation.