--STEWART, DUGALD. _The Elements of the Philosophy of the Human Mind, Part 3, chap. 1, sect. 3._ =243.= Whenever ... a controversy arises in mathematics, the issue is not whether a thing is true or not, but whether the proof might not be conducted more simply in some other way, or whether the proposition demonstrated is sufficiently important for the advancement of the science as to deserve especial enunciation and emphasis, or finally, whether the proposition is not a special case of some other and more general truth which is as easily discovered.--SCHUBERT, H. _Mathematical Essays and Recreations (Chicago, 1898), p. 28._ =244.= ... just as the astronomer, the physicist, the geologist, or other student of objective science looks about in the world of sense, so, not metaphorically speaking but literally, the mind of the mathematician goes forth in the universe of logic in quest of the things that are there; exploring the heights and depths for facts--ideas, classes, relationships, implications, and the rest; observing the minute and elusive with the powerful microscope of his Infinitesimal Analysis; observing the elusive and vast with the limitless telescope of his Calculus of the Infinite; making guesses regarding the order and internal harmony of the data observed and collocated; testing the hypotheses, not merely by the complete induction peculiar to mathematics, but, like his colleagues of the outer world, resorting also to experimental tests and incomplete induction; frequently finding it necessary, in view of unforeseen disclosures, to abandon one hopeful hypothesis or to transform it by retrenchment or by enlargement:--thus, in his own domain, matching, point for point, the processes, methods and experience familiar to the devotee of natural science. --KEYSER, CASSIUS J. _Lectures on Science, Philosophy and Art (New York, 1908), p. 26._