The Commens Dictionary

Quote from ‘On Quantity, with special reference to Collectional and Mathematical Infinity’

…the distinguishing characteristic of mathematics is that it is the scientific study of hypotheses which it first frames and then traces to their consequences. Mathematics is either applied or pure. Applied mathematics treats of hypotheses in the forms in which they are first suggested by experience, involving more or less of features which have no bearing upon the forms of deduction of consequences from them. Pure mathematics is the result of an afterthought by which these irrelevant features are eliminated.