Immanuel Kant on Mathematics

“The science of mathematics presents the most brilliant example of how pure reason may successfully enlarge its domain without the aid of experience.”

“Those who thought they could distinguish philosophy from mathematics by saying that the former was concerned with quality only, the latter with quantity only, mistook effect for cause. It is owing to the form of mathematical knowledge that it can refer to quanta only, because it is only the concept of quantities that admits of construction, that is, of a priori representation in intuition, while qualities cannot be represented in any but empirical intuition.”

“I maintain that in every special natural doctrine only so much science proper is to be met with as mathematics; for... science proper, especially of nature, requires a pure portion, lying at the foundation of the empirical, and based upon à priori knowledge of natural things. ...the conception should be constructed. But the cognition of the reason through construction of conceptions is mathematical. A pure philosophy of nature in general, namely, one that only investigates what constitutes a nature in general, may thus be possible without mathematics; but a pure doctrine of nature respecting determinate natural things (corporeal doctrine and mental doctrine), is only possible by means of mathematics; and as in every natural doctrine only so much science proper is to be met with therein as there is cognition à priori, a doctrine of nature can only contain so much science proper as there is in it of applied mathematics.”