=648.= Let him [the author] be permitted also in all humility to add ... that in consequence of the large arrears of algebraical and arithmetical speculations waiting in his mind their turn to be called into outward existence, he is driven to the alternative of leaving the fruits of his meditations to perish (as has been the fate of too many foregone theories, the still-born progeny of his brain, now forever resolved back again into the primordial matter of thought), or venturing to produce from time to time such imperfect sketches as the present, calculated to evoke the mental co-operation of his readers, in whom the algebraical instinct has been to some extent developed, rather than to satisfy the strict demands of rigorously systematic exposition. --SYLVESTER, J. J. _Philosophic Magazine (1863), p. 460._ =649.= In other branches of science, where quick publication seems to be so much desired, there may possibly be some excuse for giving to the world slovenly or ill-digested work, but there is no such excuse in mathematics. The form ought to be as perfect as the substance, and the demonstrations as rigorous as those of Euclid. The mathematician has to deal with the most exact facts of Nature, and he should spare no effort to render his interpretation worthy of his subject, and to give to his work its highest degree of perfection. “_Pauca sed matura_” was Gauss’s motto.--GLAISHER, J. W. L. _Presidential Address British Association for the Advancement of Science, Section A, (1890); Nature, Vol. 42, p. 467._ =650.= It is the man not the method that solves the problem. --MASCHKE, H. _Present Problems of Algebra and Analysis; Congress of Arts and Sciences (New York and Boston, 1905), Vol. 1, p. 530._ =651.= Today it is no longer questioned that the principles of the analysts are the more far-reaching. Indeed, the synthesists lack two things in order to engage in a general theory of algebraic configurations: these are on the one hand a definition of imaginary elements, on the other an interpretation of general algebraic concepts. Both of these have subsequently been developed in synthetic form, but to do this the essential principle of synthetic geometry had to be set aside. This principle which manifests itself so brilliantly in the theory of linear forms and the forms of the second degree, is the possibility of immediate proof by means of visualized constructions.--KLEIN, FELIX. _Riemannsche Flächen (Leipzig, 1906), Bd. 1, p. 234._