=816.= Whoever limits his exertions to the gratification of others, whether by personal exhibition, as in the case of the actor and of the mimic, or by those kinds of literary composition which are calculated for no end but to please or to entertain, renders himself, in some measure, dependent on their caprices and humours. The diversity among men, in their judgments concerning the objects of taste, is incomparably greater than in their speculative conclusions; and accordingly, a mathematician will publish to the world a geometrical demonstration, or a philosopher, a process of abstract reasoning, with a confidence very different from what a poet would feel, in communicating one of his productions even to a friend.--STEWART, DUGALD. _Elements of the Philosophy of the Human Mind, Part 3, chap. 1, sect. 3._ =817.= Considering that, among all those who up to this time made discoveries in the sciences, it was the mathematicians alone who had been able to arrive at demonstrations--that is to say, at proofs certain and evident--I did not doubt that I should begin with the same truths that they have investigated, although I had looked for no other advantage from them than to accustom my mind to nourish itself upon truths and not to be satisfied with false reasons.--DESCARTES. _Discourse upon Method, Part 2; Philosophy of Descartes [Torrey] (New York, 1892), p. 48._ =818.= When the late Sophus Lie ... was asked to name the characteristic endowment of the mathematician, his answer was the following quaternion: Phantasie, Energie, Selbstvertrauen, Selbstkritik.--KEYSER, C. J. _Lectures on Philosophy, Science and Art (New York, 1908), p. 31._ =819.= The existence of an extensive Science of Mathematics, requiring the highest scientific genius in those who contributed to its creation, and calling for the most continued and vigorous exertion of intellect in order to appreciate it when created, etc.--MILL, J. S. _System of Logic, Bk. 2, chap. 4, sect. 4._ =820.= It may be true, that men, who are _mere_ mathematicians, have certain specific shortcomings, but that is not the fault of mathematics, for it is equally true of every other exclusive occupation. So there are _mere_ philologists, _mere_ jurists, _mere_ soldiers, _mere_ merchants, etc. To such idle talk it might further be added: that whenever a certain exclusive occupation is _coupled_ with specific shortcomings, it is likewise almost certainly divorced from certain _other_ shortcomings.--GAUSS. _Gauss-Schumacher Briefwechsel, Bd. 4, (Altona, 1862), p. 387._