Why did mathematicians name a functional that assigns number to function as a "distribution"?

Question

Why did people name it as a "distribution"? I don't see the reason. My instructor told us don't bother with this strange name, but I guess maybe I will have a better understanding if I know the reasons for the naming.

Answer 1

As Artem and Will Jagy have pointed out, the Wikipedia article you linked to explains that

According to his autobiography, Schwartz introduced the term "distribution" by analogy with a distribution of electrical charge, possibly including not only point charges but also dipoles and so on.

One can also look up Jeff Miller's Earliest Known Uses of Some of the Words of Mathematics, where the entry for distribution states,

Distribution in the sense of a generalized function was introduced by Laurent Schwartz in his paper Généralisation de la notion de fonction, de dérivation, de transformation de Fourier et applications mathématiques et physiques (1945).

Indeed, in the first paragraph of section 1 of Schwartz's paper we have (translated):

Thus $\delta(x)$ is not a function, it is a measure or distribution of mass, of a particularly simple type: it consists of a mass $+1$ placed at the origin.