Although social decisions are universal, very little work was completed in Russia and the Soviet Union on the theory of social choice up until recent times. Thus I am first going to discuss briefly the history of social choice in Russia. I restrict myself to the period up to 1991, since I believe this was the year in which a new era in Russian history began. The development of social choice after 1991 is a subject for future investigation.

At 1948, L.V.Kantorovich extended Newton method for solving nonlinear equations to functional spaces. This event can not be overestimated: Newton-Kantorovich method became a powerful tool in numerical analysis as well as in pure mathematics. We address the basic ideas of the method in historical perspective and focus on recent applications and extensions of the method and some approaches to overcome its local nature.