The Commens Dictionary
Quote from ‘On Quantity, with special reference to Collectional and Mathematical Infinity’
…the mathematician is not concerned with real truth, but only studies the substance of hypotheses. [—] …the mathematician observes nothing but the diagrams he himself constructs; and no occult compulsion governs his hypotheses except one from the depths of mind itself.
Thus, 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 […] the study of the substance of hypotheses, or mental creations, with a view to the drawing of necessary conclusions.