In mathematics we find the primitive source of rationality; and to mathematics must the biologists resort for means to carry out their researches.
Mechanics is the paradise of the mathematical sciences, because by means of it one comes to the fruits of mathematics.
Thus metaphysics and mathematics are, among all the sciences that belong to reason, those in which imagination has the greatest role.
A man should be learned in several sciences, and should have a reasonable, philosophical and in some measure a mathematical head, to be a complete and excellent poet.
In questions of science the authority of a thousand is not worth the humble reasoning of an individual.
Mathematics is the queen of the sciences, and number theory the queen of mathematics.
Mathematics is not a deductive science—that’s a cliché. When you try to prove a theorem, you don’t just list the hypotheses, and then start to reason. What you do is trial and error, experimentation, guess-work.
In most sciences one generation tears down what another has built and what one has established another undoes. In mathematics alone each generation adds a new story to the old structure.
Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned upon the connection of its parts.
Geometry is the only science that it hath pleased God hitherto to bestow on mankind.
Mathematics is the science of what is clear by itself.
[The] sole end of science is the honor of the human mind, and…under this title a question about numbers is worth as much as a question about the system of the world.
All the pictures which science now draws of nature and which alone seem capable of according with observational fact are mathematical pictures…From the intrinsic evidence of his creation, the Great Architect of the Universe now begins to appear as a pure mathematician.
As are the crests on the heads of peacocks, as are the gems on the hoods of cobras, so is mathematics at the top of all sciences.
SOURCE: The Yajurveda, (c. 600 BCE)
The scientist does not study nature because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful. If nature were not beautiful, it would not be worth knowing, and if nature were not worth knowing, life would not be worth living.
If all art aspires to the condition of music, all the sciences aspire to the condition of mathematics.
For the formal science of mathematics is not a positive science for the cognition of a real object, so much as an organon and aid for other sciences, which, however, as such, is both excellent in itself, and admits of many useful applications.
SOURCE: The Philosophy of Life, and Philosophy of Language, In a Course of Lectures