History of the function concept

The mathematical concept of a function dates from the 17th century in connection with the development of the calculus; for example, the slope ${\displaystyle \operatorname {d} \!y/\operatorname {d} \!x}$ of a graph at a point was regarded as a function of the x-coordinate of the point. Functions were not explicitly considered in antiquity, but some precursors of the concept can perhaps be seen in the work of medieval philosophers and mathematicians such as Oresme.

Mathematicians of the 18th century typically regarded a function as being defined by an analytic expression. In the 19th century, the demands of the rigorous development of analysis by Weierstrass and others, the reformulation of geometry in terms of analysis, and the invention of set theory by Cantor, eventually led to the much more general modern concept of a function as a single-valued mapping from one set to another.