The essence of mathematics lies in its freedom.

CANTOR, GEORGE.
Mathematische Annalen, Bd. 21, p. 564-

***

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 (Tubingen, 1884), P- 16.

****

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 attgemeinen Manigfaltigkeits-
lehre (Leipzig, 1883), Sect. 8.

***

Mathematics is not a careful march down a well-cleared highway, but a journey into a strange wilderness, where the explorers often get lost.  Rigour should be a signal to the historian that the maps have been made, and the real explorers have gone elsewhere.  ~W.S. Anglin