What Is the History of Function Notation?

Functions have been represented throughout history in both mathematical expressions and words.

The basics of algebra focus on the function, a general term that has come to have precise, mathematical meanings. Throughout the centuries, mathematicians have explored the idea of the function and developed ways to represent it.

Early Origins of the Concept

The first people to work with functions did so through their mathematics and did not call these types of relationships by a specific name. The Babylonians first illustrated the concept of a function as a relationship between two data sets with tables. Later, a Greek mathematician named Ptolemy demonstrated his knowledge of functions through his work in trigonometry.

Use of the Term Function

Like other mathematicians of the 17th century and earlier, Rene Descartes used the term "function" loosely to refer to a variety of mathematical relationships. Over time, the word took on a more and more specific meaning. Writings between Gottfried Wilhelm Leibniz and Johann Bernoulli in the late 17th century indicate a use of the term that corresponds to its modern meaning.

Function

In 1748, the term function took on its most specific and final form when Leonhard Euler included a definition of it in his book, "Introductio in Analysin Infinitorum." Euler also introduced the mathematical notation that describes a function: y = f(x).

References

• The MacTutor History of Mathematics Archive: Functions
• Science Encyclopedia: History of Functions