=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._ =1512.= Besides the exercise in keen comprehension and the certain discovery of truth, mathematics has another formative function, that of equipping the mind for the survey of a scientific system.--GRASSMANN, H. _Stücke aus dem Lehrbuche der Arithmetik; Werke (Leipzig, 1904), Bd. 2, p. 298._ =1513.= Mathematicks may help the naturalists, both to frame hypotheses, and to judge of those that are proposed to them, especially such as relate to mathematical subjects in conjunction with others.--BOYLE, ROBERT. _Works (London, 1772), Vol. 3, p. 429._ =1514.= The more progress physical sciences make, the more they tend to enter the domain of mathematics, which is a kind of centre to which they all converge. We may even judge of the degree of perfection to which a science has arrived by the facility with which it may be submitted to calculation.--QUETELET.