Who first introduced the concept of mathematical functions?
History of the function concept
The term "function" was literally introduced by Gottfried Leibniz, in a 1673 letter, to describe a quantity related to points of a curve, such as a coordinate or curve's slope.[9] Johann Bernoulli started calling expressions made of a single variable "functions." In 1698, he agreed with Leibniz that any quantity formed "in an algebraic and transcendental manner" may be called a function of x.[10] By 1718, he came to regard as a function "any expression made up of a variable and some constants."[11] Alexis Claude Clairaut (in approximately 1734) and Leonhard Euler introduced the familiar notation f ( x ) {\displaystyle {f(x)}} for the value of a function.[12]
Sergei Sobolev
Sobolev introduced notions that are now fundamental for several areas of mathematics. Sobolev spaces can be defined by some growth conditions on the Fourier transform. They and their embedding theorems are an important subject in functional analysis. Generalized functions (later known as distributions) were first introduced by Sobolev in 1935 for weak solutions, and further developed by Laurent Schwartz. Sobolev abstracted the classical notion of differentiation, so expanding the range of application of the technique of Newton and Leibniz. The theory of distributions is considered now as the calculus of the modern epoch.