Prominent Russian mathematician Academician Leonid Vital’evich Kantorovich (1912–1986) is the only Nobel laureate in Economics representing Russian Federation / Soviet Union [1], [2], [3]. Almost all the achievements of L. V. Kantorovich in economical theory had a mathematical basis. Back in 1938, when L. V. Kantorovich was solving a specific problem of loading industrial equipment, a young mathematician found a solution to this problem, but along the way discovered that a wide class of industrial problems lends itself to a clear mathematical formulation (and further solution). This is how the foundations were laid for a fundamentally new direction at the intersection of mathematics and economics — linear programming, which made it possible to quantitatively approach many problems of the economy and solve them by numerical methods. 2. In our communication, we consider the mathematical foundations of the contribution of L. V. Kantorovich in economical theory. At the same time, we do not limit ourselves to the consideration of linear programming (one of the founders of which, as we have already mentioned, this mathematician is), but we will also give some applications from mathematical analysis, computational mathematics, discrete mathematics, etc.