An Essay concerning Human Understanding, Bk. 4, chap. 2, sect. 9.
[1442]. Now I shall remark again what I have already touched upon more than once, that it is a common opinion that only mathematical sciences are capable of a demonstrative certainty; but as the agreement and disagreement which may be known intuitively is not a privilege belonging only to the ideas of numbers and figures, it is perhaps for want of application on our part that mathematics alone have attained to demonstrations.—Leibnitz.
New Essay concerning Human Understanding, Bk. 4, chap. 2, sect. 9 [Langley].
CHAPTER XV
MATHEMATICS AND SCIENCE
[1501]. How comes it about that the knowledge of other sciences, which depend upon this [mathematics], is painfully sought, and that no one puts himself to the trouble of studying this science itself? I should certainly be surprised, if I did not know that everybody regarded it as being very easy, and if I had not long ago observed that the human mind, neglecting what it believes to be easy, is always in haste to run after what is novel and advanced.—Descartes.
Rules for the Direction of the Mind; Philosophy of Descartes [Torrey], (New York, 1892), p. 72.
[1502]. All quantitative determinations are in the hands of mathematics, and it at once follows from this that all speculation which is heedless of mathematics, which does not enter into partnership with it, which does not seek its aid in distinguishing between the manifold modifications that must of necessity arise by a change of quantitative determinations, is either an empty play of thoughts, or at most a fruitless effort. In the field of speculation many things grow which do not start from mathematics nor give it any care, and I am far from asserting that all that thus grow are useless weeds, among them may be many noble plants, but without mathematics none will develop to complete maturity.—Herbart, J. F.
Werke (Kehrbach), (Langensalza, 1890), Bd. 5, p. 106.