Mathematics #263445

IN the early part of the last century a philosophic French mathematician, addressing himself to the question of the perfectibility of scientific doctrines, expressed the opinion that one may not imagine the last word has been said of a given theory so long as it can not by a brief explanation be made clear to the man of the street. Doubtless that concep tion of doctrinal perfectibility, taken literally, can never be realized. For doubtless, just as there exist now, so in the f u ture there Will abound, even in greater and greater variety and on a vaster and vaster scale, deep-laid and high-tower ing scientific doctrines that, in respect to their infinitude of detail and in their remoter parts and more recondite strue ture, shall not be intelligible to any but such as concen trate their life upon them. And so the noble dream of Gergonne can never literally come true. Nevertheless, as an ideal, as a goal of aspiration, it is of the highest value, and, though in no case can it be quite attained, it yet admits in many, as I believe, of a surprisingly high degree of ap proximation. I do not mind frankly owning that I do not share in the feeling of those, if there be any such, who re gard their special subjects as so intricate, mysterious and high, that in all their sublimer parts they are absolutely in accessible to the profane man of merely general culture even When he is led by the hand of an expert and conde scending guide. For scientific theories are, each and all of them, and they will continue to be, built upon and aboutnotions which, however sublimated, are nevertheless de rived from common sense. These etherealized central con cepts, together with their manifold bearings on the higher interests of life and general thought, can be measurably as similated to the language of the common level from which they arose. And, in passing, I should like to express the hope that here at Columbia there may one day be estab lished a magazine that shall have for its aim to mediate, by the help, if it may be found, of such pens as those of Hux ley and Clifford, between the focal concepts and the larger aspects of the technical doctrines of the Specialist, on the one hand, and the teeming curiosity, the great listening, waiting, eager, hungering consciousness of the educated thinking public on the other. Such a service, however, is not to be lightly undertaken. An hour, at all events, is hardly time enough in which to conduct an excursion even of scientific folk through the mazes of more than twenty hundred years of mathematical thought or even to express intelligibly, if one were competent, the significance of the whole in a critical estimate.