Schriften (Berlin, 1901), Teil 2, p. 222.
[1508]. I contend, that each natural science is real science only in so far as it is mathematical.... It may be that a pure philosophy of nature in general (that is, a philosophy which concerns itself only with the general concepts of nature) is possible without mathematics, but a pure science of nature dealing with definite objects (physics or psychology), is possible only by means of mathematics, and since each natural science contains only as much real science as it contains a priori knowledge, each natural science becomes real science only to the extent that it permits the application of mathematics.—Kant, E.
Metaphysische Anfangsgründe der Naturwissenschaft, Vorrede.
[1509]. The theory most prevalent among teachers is that mathematics affords the best training for the reasoning powers;... The modern, and to my mind true, theory is that mathematics is the abstract form of the natural sciences; and that it is valuable as a training of the reasoning powers, not because it is abstract, but because it is a representation of actual things.—Safford, T. H.
Mathematical Teaching etc. (Boston, 1886), p. 9.
[1510]. It seems to me that no one science can so well serve to co-ordinate and, as it were, bind together all of the sciences as the queen of them all, mathematics.—Davis, E. W.
Proceedings Nebraska Academy of Sciences for 1896 (Lincoln, 1897), p. 282.
[1511]. And as for Mixed Mathematics, I may only make this prediction, that there cannot fail to be more kinds of them, as nature grows further disclosed.—Bacon, Francis.
Advancement of Learning, Bk. 2; De Augmentis, Bk. 3.