David E Smith - Collected Quotes

"The whole history of the development of mathematics has been a history of the destruction of old definitions, old hobbies, old idols." (David E Smith, American Mathematical Monthly, Vol. 1, No 1, 1894)

"It is doubtful if we have any other subject that does so much to bring to the front the danger of carelessness, of slovenly reasoning, of inaccuracy, and of forgetfulness as this science of geometry, which has been so polished and perfected as the centuries have gone on." (David E Smith, "The Teaching of Geometry", 1911)

"We study art because we receive pleasure from the great works of the masters, and probably we appreciate them the more because we have dabbled a little in pigments or in clay. We do not expect to be composers, or poets, or sculptors, but we wish to appreciate music and letters and the fine arts, and to derive pleasure from them and be uplifted by them. […] So it is with geometry. We study it because we derive pleasure from contact with a great and ancient body of learning that has occupied the attention of master minds during the thousands of years in which it has been perfected, and we are uplifted by it." (David E Smith, "The Teaching of Geometry", 1911)

"Our work is great in the classroom it we feel the nobility of that work, if we love the human souls we work with more than the division of fractions, if we love our subject so much that we make our pupils love it, and if we remember that our duty to the world is to help fix in the minds of our pupils the facts of number that they must have in after life." (David E Smith, "The Progress of Arithmetic", 1923) 

"We have come to believe that a pupil in school should feel that he is living his own life naturally. with a minimum of restraint and without tasks that are unduly irksome; that he should find his way through arithmetic largely hoy his own spirit of curiosity; and that he should be directed in arithmetic as he would he directed in any other game, - not harshly driven, hardly even led, but proceeding with the feeling that he is being accompanied and that he is doing his share in finding the way." (David E Smith, "The Progress of Arithmetic", 1923)

"Mathematics, indeed, is the very example of brevity, whether it be in the shorthand rule of the circle, c = πd, or in that fruitful formula of analysis, e^iπ = -1, — a formula which fuses together four of the most important concepts of the science — the logarithmic base, the transcendental ratio π, and the imaginary and negative units." (David E Smith, "The Poetry of Mathematics", The Mathematics Teacher, 1926)

"If we are to teach mathematics at all, real success is not possible unless we know that the subject is beautiful as well as useful." (David E Smith, "The Poetry of Mathematics and Other Essays", 1934)

"[…] the merit of mathematics, in all its forms, consists in its truth; truth conveyed to the understanding, not directly by words but by symbols which serve as the world’s only universal written language." (David E Smith, "The Poetry of Mathematics and Other Essays", 1934)

"One merit of mathematics few will deny: it says more in fewer words than any other science. The formula, e^iπ = -1 expressed a world of thought, of truth, of poetry, and of the religious spirit ‘God eternally geometrizes’." (David E Smith, "The Poetry of Mathematics and Other Essays", 1934)

"One thing that mathematics early implants, unless hindered from so doing, is the idea that here, at last, is an immortality that is seemingly tangible - the immortality of a mathematical law." (David E Smith, "The Poetry of Mathematics and Other Essays", 1934)

"We cannot convey mathematics to the great mass of people unless we first dwell upon the utility of the subject and imagine what would happen to the world if every trace of mathematics and of mathematical knowledge should cease to exist." (David E Smith, "The Poetry of Mathematics and Other Essays", 1934)

"What, after all, is mathematics but the poetry of the mind, and what is poetry but the mathematics of the heart?" (David E Smith)