=404.= Mathematics is a type of thought which seems ingrained in the human mind, which manifests itself to some extent with even the primitive races, and which is developed to a high degree with the growth of civilization.... A type of thought, a body of results, so essentially characteristic of the human mind, so little influenced by environment, so uniformly present in every civilization, is one of which no well-informed mind today can be ignorant.--YOUNG, J. W. A. _The Teaching of Mathematics (London, 1907), p. 14._ =405.= Probably among all the pursuits of the University, mathematics pre-eminently demand self-denial, patience, and perseverance from youth, precisely at that period when they have liberty to act for themselves, and when on account of obvious temptations, habits of restraint and application are peculiarly valuable.--TODHUNTER, ISAAC. _The Conflict of Studies and other Essays (London, 1873), p. 12._ =406.= Mathematics renders its best service through the immediate furthering of rigorous thought and the spirit of invention. --HERBART J. F. _Mathematischer Lehrplan für Realschulen: Werke [Kehrbach] (Langensalza, 1890), Bd. 5, p. 170._ =407.= It seems to me that the older subjects, classics and mathematics, are strongly to be recommended on the ground of the accuracy with which we can compare the relative performance of the students. In fact the definiteness of these subjects is obvious, and is commonly admitted. There is however another advantage, which I think belongs in general to these subjects, that the examinations can be brought to bear on what is really most valuable in these subjects.--TODHUNTER, ISAAC. _Conflict of Studies and other Essays (London, 1873), pp. 6, 7._ =408.= It is better to teach the child arithmetic and Latin grammar than rhetoric and moral philosophy, because they require exactitude of performance it is made certain that the lesson is mastered, and that power of performance is worth more than knowledge.--EMERSON, R. W. _Lecture on Education._