It is symbolic that in that same year of 1935, S.L. Sobolev, who was 26 years old that time, submitted to the editorial board of the journal “Matematicheskiy sbornik” his famous work 61 and published at the same time its brief version in “Doklady AN SSSR’’ 60. This work laid foundations of a completely new outlook on the concept of function, unexpected even for N.N. Luzin — the concept of a generalized function (in the framework of the notion of distribution introduced later). It is also symbolic that the work by Sobolev was devoted to the Cauchy problem for hyperbolic equations and, in particular, to the same vibrating string.
In recent years Luzin’s assertion that the discussion concerning the notion of function is continuing was confirmed once again, and the stimulus for the development of this fundamental concept of mathematics is, as it was before, the equations of mathematical physics (see, in particular, Addition written by Yu.V. Egorov and 10, 11, 16, 17, 18, 32, 49, 67).
This special role of the equations of mathematical physics (in other words, partial differential equations directly connected with natural phenomena) is explained by the fact that they express the mathematical essence of the fundamental laws of the natural sciences and consequently are a source and stimulus for the development of fundamental mathematical concepts and theories.