Jacob W A Young - Collected Quotes

"All thinking and all actions are influenced by conclusions that have been consciously or unconsciously drawn." (Jacob W A Young, "The Teaching of Mathematics", 1907)

"Little can be understood of even the simplest phenomena of nature without some knowledge of mathematics, and the attempt to penetrate deeper into the mysteries of nature compels simultaneous development of the mathematical processes." (Jacob W A Young, "The Teaching of Mathematics", 1907)

"Mathematics has beauties of its own - a symmetry and proportion in its results, a lack of superfluity, an exact adaptation of means to ends, which is exceedingly remarkable and to be found elsewhere only in the works of the greatest beauty." (Jacob W A Young, "The Teaching of Mathematics", 1907)

"Mathematics makes constant demands upon the imagination, calls for picturing in space (of one, two, three dimensions), and no considerable success can be attained without a growing ability to imagine all the various possibilities of a given case, and to make them defile before the mind's eye." (Jacob W A Young, "The Teaching of Mathematics", 1907)

"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." (Jacob W A Young, "The Teaching of Mathematics", 1907)

"One of these modes of thought is the ability to grasp a situation, to seize the facts, and to perceive correctly the state of affairs. […] The web of facts and relationships in which every one moves is moreover extremely tangled. Much practice is requisite to even fair success in grasping situations, and we look to the school to furnish and direct such practice. Mathematics is specially adapted to the beginning of the practice because its facts are few and uncomplicated." (Jacob W A Young, "The Teaching of Mathematics", 1907)

"So completely is nature mathematical that some of the more exact natural sciences, in particular astronomy and physics, are in their theoretic phases largely mathematical in character, while other sciences which have hitherto been compelled by the complexity of their phenomena and the inexactitude of their data to remain descriptive and empirical, are developing towards the mathematical ideal, proceeding upon the fundamental assumption that mathematical relations exist between the forces and the phenomena, and that nothing short, of the discovery and formulations of these relations would constitute definitive knowledge of the subject. Progress is measured by the closeness of the approximation to this ideal formulation." (Jacob W A Young, "The Teaching of Mathematics", 1907)

"Still more important than x the subject matter of mathematics is the fact that it exemplifies 'most typically, clearly and simply certain modes of thought which are of the utmost importance to every one." (Jacob W A Young, "The Teaching of Mathematics", 1907)

"The training which mathematics gives in working with symbols is an excellent preparation for other sciences; […] the world's work requires constant mastery of symbols." (Jacob W A Young, "The Teaching of Mathematics", 1907)

"The type of reasoning found in mathematics seems thus not only available but essentially interwoven with every inference in non-mathematical reasoning, being always used in one of its two steps ; facility in making the other step, the more difficult one, must be attained through other than purely mathematical training." (Jacob W A Young, "The Teaching of Mathematics", 1907)

"There is one, but only one branch which may claim certainty; in which experts have not seriously disagreed, - Mathematics. […] Mathematics possesses also the second desideratum, - Simplicity. It begins, as is well known, with few and uncomplicated definitions and postulates, and proceeds, step by step, to quite elaborate cases. […] Mathematics possesses also the third desideratum, - Applicability of the skill acquired." (Jacob W A Young, "The Teaching of Mathematics", 1907)