The Duty of Exposition with Special Reference to the Cauchy-Heaviside Expansion Theorem

Abstract

As the speaker representing the Mathematical Association of America at this session I propose this morning to call your attention to one of the more important duties of a mathematician, namely, the duty of explaining as clearly as possible mathematical truths and discoveries both to his fellow mathematicians and to students of mathematics in general. The American Mathematical Society is especially devoted to the encouragement of research and the secretary of that society has called to your attention during this meeting the remarkable increase in the number of papers presented annually to the Society during the past five years. This increase has been such as to make the problem of publishing the results of mathematical research in America a very acute and difficult one. At the same time it has become more desirable than ever before that the papers published in our American journals should be as clear and as easily readible as possible. The Mathematical Association of America is especially concerned with the teaching and exposition of mathematical truth and it is pretty generally agreed that it is highly desirable that care should be taken to make this teaching and exposition to students as good as possible. I fear, however, that some of my friends who are particularly interested in research agree to this in a rather condescending manner; their tone implying that, whilst nothing should be done to discourage anyone beginning the study of mathematics, such care is not so necessary nor even so desirable when writing for fellow mathematicians. The underlying idea is that a competent mathematician usually prefers to glance at a paper, see the results arrived at, and then derive these results in his own individual manner. I believe that this opinion is not justified by the facts and in support of this belief I shall mention two instances which have recently come to my attention where mathematicians of great competence failed, through a lack of detail or of clarity in available expositions of known results, to arrive at immediate and important corollaries of these results. I shall be happy if my talk this morning tends to make the editors of our mathematical journals insist more definitely on clearness of exposition when considering papers submitted for publication. One can surmise that the writers of at least some of our papers set down their results with the referee of the paper more in mind than the prospective readers. They neglect, therefore, to state or. emphasize points which they think will be familiar to the referee. Of course this is unfortunate since there is us'ually a one-to-one