Full Idea
Pure mathematics is the class of all propositions of the form 'p implies q', where 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.
Gist of Idea
Pure mathematics is the class of propositions of the form 'p implies q'
Source
Bertrand Russell (The Principles of Mathematics [1903], §001)
Book Reference
Russell,Bertrand: 'Principles of Mathematics' [Routledge 1992], p.3
A Reaction
Linnebo calls Russell's view here 'deductive structuralism'. Russell gives (§5) as an example that Euclid is just whatever is deduced from his axioms.