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… - Christian Heinrich Dillmann

Mathematics, too, is a language, and as concerns its structure and content it is the most perfect language which exists, superior to any vernacular; indeed, since it is understood by every people, mathematics may be called the language of languages. Through it, as it were, nature herself speaks; through it the Creator of the world has spoken, and through it the Preserver of the world continues to speak.

It is known that the mathematics prescribed for the high school [Gymnasien] is essentially Euclidean, while it is modern mathematics, the theory of functions and the infinitesimal calculus, which has secured for us an insight into the mechanism and laws of nature. Euclidean mathematics is indeed, a prerequisite for the theory of functions, but just as one, though he has learned the inflections of Latin nouns and verbs, will not thereby be enabled to read a Latin author much less to appreciate the beauties of a Horace, so Euclidean mathematics, that is the mathematics of the high school, is unable to unlock nature and her laws. Euclidean mathematics assumes the completeness and invariability of mathematical forms; these forms it describes with appropriate accuracy and enumerates their inherent and related properties with perfect clearness, order, and completeness, that is, Euclidean mathematics operates on forms after the manner that anatomy operates on the dead body and its members.

It is number which regulates everything and it is measure which establishes universal order.... A quiet peace, an inviolable order, an inflexible security amidst all change and turmoil characterize the world which mathematics discloses and whose depths it unlocks.