Why Study Mathematics?

The value of that rigorous mental training which is obtained from the study of mathematics has long been recognized, although that special kind of mental gymnastics is as painful to the ordinary student as physical training to a rheumatic. But the recent change in the college curriculum which practically makes mathematics required for all freshmen, was made, I feel sure, not only to give freshmen the benefit of such training, but also to make it possible to carry on the work in advanced classes. In other words, a knowledge of at least the elementary mathematics given the first year, has become a necessity if one is to be anything more than an amateur student.

This is particularly true of the sciences. For instance, to attempt to study astronomy without a knowledge of mathematics is like reading "Hamlet with Hamlet left out." One may take a descriptive course, which is nothing more or less than a geography of the heavens, but that is not astronomy. One may spend hours in a physical laboratory measuring heat or electric currents, but this is not physics. To get any definite idea of the fundamental principles of these sciences, one should have a thorough knowledge of mechanics and other elementary mathematics. In some of the scientific schools calculus is being introduced in the freshmen year, because the economists complain that they are unable to teach more than the mere elements of their science without presupposing a knowledge of calculus and analytic geometry. I inquired in a university library not long ago for a certain book on Differential Equations and found that it was in daily use in the psychological laboratory. These new sciences are being put on a firm foundation of which mathematics is a corner stone.

As a study of mathematics will always from the very nature of things be unpopular, and the number for which it has its own peculiar charm, always has been and always will be small. But those who pride themselves on being general students, who wish to do something more than dabble at education, should study mathematics because it is of fundamental importance, just as one studies the languages in order to read the masterpieces of literature.