Learn English – the historical origin for the naming of the word ‘function’ in its mathematical context

etymologyhistorymathematicssemantics

I tried Wikipedia but it doesn't explain why functions are called functions.

The reason why I'm asking is because this word just doesn't make any sense for what it does.

If we were to reinvent all the words that don't make sense, and they become normal in a given culture, communication would be far more efficient and clear.

Best Answer

This is what OED has to say about the origin:

This use of the Latin functio is due to Leibniz and his associates. A paper in the Acta Eruditorum for 1692, pp. 169–170, signed ‘O.V.E.’, but probably written by Leibniz, uses functiones in a sense hardly different from its ordinary untechnical sense, to denote the various ‘offices’ which a straight line may fulfil in relation to a curve, viz. its tangent, normal, etc. In the same journal for 1694, p. 316, Leibniz defines functio as ‘a part of a straight line which is cut off by straight lines drawn solely by means of a fixed point, and of a point in the curve which is given together with its degree of curvature’; the examples given being the ordinate, abscissa, tangent, normal, etc. As the functiones (in Leibniz' sense) of a curve are variable quantities having a fixed mutual relation, this use of the word easily developed into the modern sense, which occurs in the writings of the Bernoullis early in the 18th cent. A somewhat peculiar use occurs about 1713, in Leibniz' Hist. et Origo Calc. Diff. (Math. Schriften ed. Gerhardt V. 408), where he says that just as constant quantities have their ‘functions’, viz. powers and roots, so variables have also ‘functions’ of a third kind, viz. differentials.

Acta Eruditorum can be found here, but it's in Latin.

A quote taken from the website Earliest Known Uses of Some of the Words of Mathematics indicates that there is an earlier use by Leibniz, in 1673:

The word FUNCTION first appears in a Latin manuscript "Methodus tangen tium inversa, seu de fuctionibus" written by Gottfried Wilhelm Leibniz (1646-1716) in 1673. Leibniz used the word in the non-analytical sense, as a magnitude which performs a special duty. He considered a function in terms of "mathematical job"- the "employee" being just a curve. He apparently conceived of a line doing "something" in a given figura... From the beginning of his manuscript, however, Leibniz demonstrated that he already possessed the idea of function, a term he denominates relatio.

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