# Early uses of the word "operator" in mathematics

I'm looking for early uses of the word "operator" in mathematics and how it evolved to become a synonym for the modern "function" in certain areas. Jeff Miller's page only has an entry for "operation" and "operand".

• "Linear operator" seems to have become widespread in 1891-1893, according to Google Books; O. Heaviside was a big user & maybe popularizer of the term. Mar 22 at 21:53

The unabridged Oxford Dictionary is of great help in such matters. It requires subscription. Here are the examples it provides since 1855.

Originally: (Mathematics) a symbol or group of symbols indicating an operation or series of operations to be carried out, usually on a following expression. Later also: a sign or symbol which effects other types of operation, as logical, phonological, syntactic, etc.

1855 R. Carmichael Treat. Calculus of Operations 3 The indetermination is due to a source quite independent of the character of the functional operator.

1925 J. M. Bryant & J. A. Correll Alternating-current Circuits iii. 74 The operator, j = √(− 1), turns the vector through 90 degrees in a counterclockwise direction each time it is used.

1952 Eng. & Germanic Stud. 4 12 We may regard Modern English stone as the result of operating with an operator that I shall write {AS. ā MnE. [ou]} on Anglo-Saxon stān.

1969 V. J. Calderbank Course on Programming in FORTRAN IV iii. 28
The relational expression..has the general form e1re2 where e1 and e2 are arithmetic expressions..being compared by one of the following relational operators, r: .EQ. Equal to (=); .LT. Less than (<); [etc.].

1990 Proc. London Math. Soc. 60 365 The centroid operator and the projection operator are quite different. For example, the centroid operator commutes with linear transformations, while the projection operator does not.