=619.= Though we must not without further consideration condemn a body of reasoning merely because it is easy, nevertheless we must not allow ourselves to be lured on merely by easiness; and we should take care that every problem which we choose for attack, whether it be easy or difficult, shall have a useful purpose, that it shall contribute in some measure to the up-building of the great edifice.--SEGRE, CORRADI. _Some Recent Tendencies in Geometric Investigation; Rivista di Matematica (1891), p. 63. Bulletin American Mathematical Society, 1904, p. 465. [Young, J. W.]._ =620.= No mathematician now-a-days sets any store on the discovery of isolated theorems, except as affording hints of an unsuspected new sphere of thought, like meteorites detached from some undiscovered planetary orb of speculation.--SYLVESTER, J. J. _Notes to the Exeter Association Address; Collected Mathematical Papers (Cambridge, 1908), Vol. 2, p. 715._ =621.= Isolated, so-called “pretty theorems” have even less value in the eyes of a modern mathematician than the discovery of a new “pretty flower” has to the scientific botanist, though the layman finds in these the chief charm of the respective sciences. --HANKEL, HERMANN. _Die Entwickelung der Mathematik in den letzten Jahrhunderten (Tübingen, 1884), p. 15._ =622.= It is, so to speak, a scientific tact, which must guide mathematicians in their investigations, and guard them from spending their forces on scientifically worthless problems and abstruse realms, a tact which is closely related to _esthetic tact_ and which is the only thing in our science which cannot be taught or acquired, and is yet the indispensable endowment of every mathematician.--HANKEL, HERMANN. _Die Entwickelung der Mathematik in den letzten Jahrhunderten (Tübingen, 1884), p. 21._ =623.= The mathematician requires tact and good taste at every step of his work, and he has to learn to trust to his own instinct to distinguish between what is really worthy of his efforts and what is not; he must take care not to be the slave of his symbols, but always to have before his mind the realities which they merely serve to express. For these and other reasons it seems to me of the highest importance that a mathematician should be trained in no narrow school; a wide course of reading in the first few years of his mathematical study cannot fail to influence for good the character of the whole of his subsequent work.--GLAISHER, J. W. L.