ADDRESS BY PROFESSOR HENRY T. EDDY, VICE PRESIDENT, SECTION A. COLLEGE MATHEMATICS. In a survey of the general interests for the advancement of which this section of Mathematics and Astronomy has now met, it has seemed to me that there is one subject in the consideration of which you all must have a vital interest. And as this is also a subject of daily professional interest to myself, and closely concerns the future welfare of this association, as well as the progress of science in our land, I may be pardoned for pressing it upon your attention and stating, so far as I may be able, the truth as it appears to me. The subject I refer to is the present state of mathematical training in our colleges; its aims, its needs, and its relations to education and to scientific research. I am the more willing to speak upon this subject because I feel that my opportunities for experience, though they perhaps have not been of so great duration as others have enjoyed, have, nevertheless, been varied, and of such a kind as possibly to be useful in awakening thought and in bringing to light the experience of others upon this important part of our college study, a part, I may say, which has been almost completely overlooked in the earnest controversy which has arisen during the past year, respecting the attitude of our colleges toward the various branches of learning, ancient and modern, embraced in their curricula. As the thoughts I have to present are based largely on personal experience, I may be pardoned for saying that this experience commenced twenty-one years ago on entering the freshman class at Yale College, and after graduation it was continued as a student in the Sheffield Scientific School. Since then it has been my lot to be constantly engaged in teaching pure and applied mathematics at first in a southern university, then four years at Cornell, one year at Princeton, and now for ten years in the University of Cincinnati, one of the youngest of our western colleges. It will be seen from this enumeration that my experience has been distributed between classical institutions on the one hand, and scientific on the other, in such a way as would naturally make my prepossessions lie in favor of the established regime of our classical colleges. If my maturer convictions have led me to criticise their method and spirit, it is not from any preconceived animosity to them, but out of a sincere desire that they may be brought to occupy a position in our educational life which shall command the undivided support of the cultivated and best informed portion of the community. One of the most unexpected revelations which this experience has made to me is that mathematical study in college is not necessarily drudgery. I think I do not state the matter too strongly when I say that during the years in which I was an undergraduate, mathematical study was regarded with deep-seated aversion by the average student, an aversion not capable of adequate expression in any ordinary way. The burial of Euclid and the cremation of analytics were a mere joke; but the inward disgust and hatred of mathematics which existed in the minds of the students of my day left an impression not to be effaced in a lifetime. Now what was the cause of such pronounced hostility? The answer is not far to seek. The study was not interesting, and it was not well understood. These are two reasons which stand in the closest possible connection with each other. We might say, either that the study failed of being understood because it was uninteresting, or that it awakened no interest because it was not well understood. Both these statements were true. I have found the same state of affairs in every classical college respecting which I have had any intimate knowledge from that day to this. In them it is an article of faith firmly held, and oft expressed by the undergraduate, that higher mathematics is a study which can be thoroughly mastered only by exceptional geniuses, of which each college class possesses of course one or more brilliant specimens ; and as to obtaining some reasonable understanding of the study, it is thought to be barely possi |