By the end of World War II, the next global confrontation emerged: the confrontation between the USA and the USSR and their allies, so between the West and the East with their antagonistic fundamental political values and their ideological contradiction. This development may be seen as a consequence of Marxism-Leninism and its claim for the world revolution or as a consequence of the political and economical structure of the USA with its permanent pursuit of new markets. All this had had also consequences for mathematicians, because the flow of information, though not completely cut, was not as easy as before. Looking positively at side effects, however, the isolated research may have not been burdened by traditional thinking and that may have been fruitful. Russian mathematicians around Pontryagin in the Steklov Institute got, with the maximum principle, new results beyond former frontiers while the Americans around Hestenes at the RAND corporation were captured by the tradition of the Chicago School of the Calculus of Variations. Nevertheless, both groups paved the way for a new field in mathematics called Optimal Control -- and their protagonists fell out with each other inside their groups.