Mathematics: The Subject and the Teacher

Abstract

These are days of change in educational affairs. Greek has almost disappeared from the curricula of school and college. It has entirely disappeared from the individual schedules of all save a mere handful of our students. The contest for the survival of Latin is being hard fought and some of its champions prophesy early failure. Very few men’s colleges in New England any longer demand for admission to the Arts course the traditional four years of Latin. The Bachelor of Science course without any Latin at all has become the common thing. We in the far east will hardly be allowed by ourselves to decide the question of the survival of Latin; the great state universities of the middle west promise to play the chief part in the solution of such educational problems, and we probably shall feel obliged to accept their verdicts. Verily “the old order changeth, yielding place to new.” Is one to see all the old-fashioned subjects drop out in their turn, and will mathematics soon depart forever from the student’s schedule? It requires no excess of confidence to answer no to this question. One notices that the onslaught of the progressives with their weapons of introductory social science, introductory general science, practical arts, community civics, typewriting, forging, and domestic science is aimed at the foreign languages, particularly Latin, and not at mathematics. A careful examination of several of those new curricula which promise to make the high school course really useful, and at the same time easy and delightful to the pupil, shows that they retain in every instance as required subjects for all students algebra and geometry. Naturally these two branches of mathematics cannot be expected to add to the ease or largely to the delight of the average boy or girl’s high school course; they are distasteful to many an earnest but non-mathematical student; they have no charm of educational novelty; yet there they stand as subjects required of all secondary school boys and girls, and why? Because they are known to be in many small ways useful subjects and in a large way necessary subjects. As to the future, one may feel sure that mathematics, which began with the first ordering of things, will not pass out from its place in our educational life until such time as order in the universe shall have given way to chaos. For mathematics, as Professor Story says, occupies a peculiar position with respect to both the arts and the sciences. It is, par excellence, an art, inasmuch as its chief function is to solve problems—not textbook examples which are merely exercises in the application of methods—but all those problems in human experience for whose correct solution sufficient data are at hand. When any line of investigation, to whatever subject it may refer, has been carried so far as to permit the application of exact reasoning, mathematics assumes control. It determines whether the results presented are consistent and whether the conclusions are valid, and it is mathematics that provides the means for applying these conclusions to the prediction of phenomena not yet observed. No science and no branch of technology is exact unless it rests on a mathematical foundation. The secrets of the future can be foretold for any science only in so far as that science is obedient to the laws of mathematics. Astronomy long ago had accumulated enough data of observation to allow its case to be submitted to the mathematician and accordingly astronomy began long ago to be an exact science. It was the mathematicians, Adams and Leverrier, who told the astronomers that their data called for another planet, and indicated to them the direction in which the astronomer should point his telescope to find it. After astronomy, next came physics, and then applied mechanics, in both of which a sound mathematical foundation has long been in building. Other sciences are in the inductive stage, still collecting material to be put in order by the mathematician as soon as the material is sufficient for the purpose. The calculus is already being applied to some of the problems of economics. The chemist employs mathematical formulas daily. The geologist, the physiologist, and the psychologist all use mathematical tools. And mathematics must continue to be used for such tasks until all science shall have become perfect and shall have passed away forever. Mathematics, then, is one of those few themes which, in Kipling’s phrase,