Sobolev of the Euler School

This is a short overview of the origins of distribution theory as well as the life of Sergĕı Sobolev (1908–1989) and his contribution to the formation of the modern outlook of mathematics. Sergĕı Lvovich Sobolev belongs to the Russian mathematical school and ranks among the scientists whose creativity has produced the major treasures of the world culture. Mathematics studies the forms of reasoning. Generally speaking, differentiation discovers the trends of a process, and integration forecasts the future from trends. The mankind of the present day cannot be imagined without integration and differentiation. The differential and integral calculus was invented by Newton and Leibniz. The fluxions of Newton and the monads of Leibniz made these giants the forerunners of the classical analysis. Euler used the concepts by Newton and Leibniz to upbring and cultivate the new mathematics of variable quantities, while making quite a few phenomenal discoveries and creating his own inexhaustible collection of miraculous formulas and theorems. Mathematical analysis remained the calculus of Newton, Leibniz, and Euler for about two hundred years. The classical calculus turned into the theory of distributions in the twentieth century. As the key objects of the modern analysis are ranked the integral in the sense of Lebesgue and the derivative in the sense of Sobolev which apply to the most general instances of interdependence that lie beyond the domains under the jurisdiction of the classical differentiation and integration. Lebesgue and Sobolev entered into history, suggesting the new approaches to the integral and derivative which expanded the sphere of influence and the scope of application of mathematics. The historic figures and discoveries deserve the historical parallels and analysis. The gift of mathematics translates from teacher to student. The endless chain of alternating generations incarnates a mathematical tradition. Characterizing a scientific school, Luzin observed that “the elder school is more precious. Indeed, any school is the collections of the creative techniques, traditions, and narrations about the past and still living scientists as well as their manners of research and views of the object of research. These narrations are collected for ages but not intended for publication or revelation to those that seem undeserving. These narrations are treasures whose power is impossible to imagine or overrate . . . . If some analogy or