Populär-wissenschafliche Vorlesungen (1908), pp. 224-225.
[204]. Pure mathematics proves itself a royal science both through its content and form, which contains within itself the cause of its being and its methods of proof. For in complete independence mathematics creates for itself the object of which it treats, its magnitudes and laws, its formulas and symbols.—Dillmann, E.
Die Mathematik die Fackelträgerin einer neuen Zeit (Stuttgart, 1889), p. 94.
[205]. The essence of mathematics lies in its freedom.—Cantor, George.
Mathematische Annalen, Bd. 21, p. 564.
[206]. Mathematics pursues its own course unrestrained, not indeed with an unbridled licence which submits to no laws, but rather with the freedom which is determined by its own nature and in conformity with its own being.—Hankel, Hermann.
Die Entwickelung der Mathematik in den letzten Jahrhunderten (Tübingen, 1884), p. 16.
[207]. Mathematics is perfectly free in its development and is subject only to the obvious consideration, that its concepts must be free from contradictions in themselves, as well as definitely and orderly related by means of definitions to the previously existing and established concepts.—Cantor, George.
Grundlagen einer allgemeinen Manigfaltigkeitslehre (Leipzig, 1883), Sect. 8.