For many parts of Nature can neither be invented with sufficient subtlety, nor demonstrated with sufficient perspicuity, nor accommodated unto use with sufficient dexterity, without the aid and intervening of the mathematics, of which sort are perspective, music, astronomy, cosmography, architecture, engineery, and divers others.
Ere land and sea and the all-covering sky Were made, in the whole world the countenance Of nature was the same, all one, well named Chaos, a raw and undivided mass, Naught but a lifeless bulk, with warring seeds Of ill-joined elements compressed together.
The physicists say that I am a mathematician, and the mathematicians say that I am a physicist. I am a completely isolated man and though everybody knows me, there are very few people who really know me.
Epistemology without contact with science becomes an empty scheme. Science without epistemology is-insofar as it is thinkable at all-primitive and muddled.
What a deep faith in the rationality of the structure of the world and what a longing to understand even a small glimpse of the reason revealed in the world there must have been in Kepler and Newton to enable them to unravel the mechanism of the heavens in long years of lonely work!
One should not understand this compulsion to construct concepts, species, forms, purposes, laws ('a world of identical cases') as if they enabled us to fix the real world; but as a compulsion to arrange a world for ourselves in which our existence is made possible:-we thereby create a world which is calculable, simplified, comprehensible, etc., for us.