Pure Mathematics is the class of all propositions of the form

where `p` implies `q`,`p` and `q` are propositions containing one or more variables, the same in the two propositions, and neither `p` nor `q` contains any constants except logical constants. And logical constants are all notions definable in terms of the following: Implication, the relation of a term to a class of which it is a member, the notion of *such that*, the notion of relation, and such further notions as may be involved in the general notion of propositions of the above form. In addition to these, mathematics *uses* a notion which is not a constituent of the propositions which it considers, namely the notion of truth.(§ 1 ¶ 1)

The Principles of Mathematics was written by Bertrand Russell, and published in in 1903. It is now available in the Public Domain.