[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.
Presidential Address British Association for the Advancement of Science, Section A, (1890); Nature, Vol. 42, p. 467.
[624]. As long as a branch of science offers an abundance of problems, so long it is alive; a lack of problems foreshadows extinction or the cessation of independent development.—Hilbert, D.
Mathematical Problems; Bulletin American Mathematical Society, Vol. 8, p. 438.