_A Budget of Paradoxes (London, 1872), p. 2._ =1538.= Among the mere talkers so far as mathematics are concerned, are to be ranked three out of four of those who apply mathematics to physics, who, wanting a tool only, are very impatient of everything which is not of direct aid to the actual methods which are in their hands.--DE MORGAN, A. _Graves’ Life of Sir William Rowan Hamilton (New York, 1882-1889), Vol. 3, p. 348._ =1539.= Something has been said about the use of mathematics in physical science, the mathematics being regarded as a weapon forged by others, and the study of the weapon being completely set aside. I can only say that there is danger of obtaining untrustworthy results in physical science, if only the results of mathematics are used; for the person so using the weapon can remain unacquainted with the conditions under which it can be rightly applied.... The results are often correct, sometimes are incorrect; the consequence of the latter class of cases is to throw doubt upon all the applications of such a worker until a result has been otherwise tested. Moreover, such a practice in the use of mathematics leads a worker to a mere repetition in the use of familiar weapons; he is unable to adapt them with any confidence when some new set of conditions arise with a demand for a new method: for want of adequate instruction in the forging of the weapon, he may find himself, sooner or later in the progress of his subject, without any weapon worth having. --FORSYTH, A. R. _Perry’s Teaching of Mathematics (London, 1902), p. 36._ =1540.= If in the range of human endeavor after sound knowledge there is one subject that needs to be practical, it surely is Medicine. Yet in the field of Medicine it has been found that branches such as biology and pathology must be studied for themselves and be developed by themselves with the single aim of increasing knowledge; and it is then that they can be best applied to the conduct of living processes. So also in the pursuit of mathematics, the path of practical utility is too narrow and irregular, not always leading far. The witness of history shows that, in the field of natural philosophy, mathematics will furnish the more effective assistance if, in its systematic development, its course can freely pass beyond the ever-shifting domain of use and application.--FORSYTH, A. R. _Presidential Address British Association for the Advancement of Science, Section A; Nature, Vol. 56 (1897), p. 377._