Note: This was republished as: Comments, Amer. Math. Monthly 100 (4) (1993), 330. The original 1913 article was published when Hedrick became editor of the Monthly.

It is not the province of the Monthly to enter the field of general pedagogy, nor will the Monthly entertain discussions that are concerned with research in general pedagogy, or that deal with new theories of pedagogy, however important these contributions may seem. Journals for the publication of such contributions abound... What we do desire is to inspire, not a discussion along these lines, but rather a discussion of definite mathematical problems... . For the discussion from this standpoint of mathematical questions, the Monthly will open its columns without reserve, except for those usual discretionary and advisory powers that are traditional in any editorship.

Note: This article was published when Hedrick became editor of the Monthly.

The lifework of hundreds of men is the teaching of collegiate mathematics; hundreds of other men are preparing for this same lifework. Thousands of students are now working and will work under the guidance of these men in collegiate courses in mathematics. Suggestions of moment arise in the minds of many, yet there exist few means for transmitting an idea in this field to others. Any organized effort toward the dissemination of methods that are new, or of facts that are interesting, in this field is totally lacking. These remarks apply, of course, only to the United States. Abroad, in every country in which mathematics holds a place commensurate with its position here, definite journals exist whose purpose is almost wholly to foster these interests. The American Mathematical Monthly, beginning with this issue, proposes to afford an opportunity for any discussions that seem valuable upon collegiate mathematics, and the editors invite contributions concerning the methods of instruction as well as those that treat special topics or theorems.

Note: This article is part of Hedrick formulating editorial policy for the Monthly.

It seems to demand an apology if we state to readers who are scientists that the basis of knowledge not received by revelation is either experimentation or deduction. As a defence for such a truism, we need only point to the many papers that show evidence of some other method of reaching conclusions. In the Dark Ages, and for a period thereafter, medical practice included the administration of blood-letting; and it was often asserted that this process was beneficial to the patient. They who first arose to demand statistics upon this and other hallowed practices were naturally regarded as heretics, and they were treated with due scorn and derision. May we very hesitatingly ask for a few statistics regarding some of our own hallowed traditions? And do we thereby incur displeasure? Shall it be said of us that we are attempting the overthrow of mathematics? In any event, that is what we mean by knowing, for we are aware of no other basis of knowledge than such experimentation as we here imply.

Note: This was written after the setting up of the Mathematical Association of America. Hedrick became president of the Association and he discusses in this quote some of the issues which led to its foundation.

No man can speak with authority concerning the future of this new Association which was created by those who met at Columbus last December. Its future lies with those who constitute its membership. Any statement must be rather a history of past events than a prediction for the future. What were the causes which led so many to wish for, to exert themselves and to struggle for a new society in the mathematical field? What motives lay behind the movement which culminated in this organization? These are questions which are distinctly answerable. I shall try to show for those who did form the Association what were their purposes and what is now their aim. If these purposes or aims are wrong or insufficient, they will perish and newer and better policies will supplant them. The great fact which we cannot overlook is that we now have a large and representative body of men and women interested in mathematics joined together in this association to foster whatever they believe to be worthy and beneficial. ... The majority of those responsible for the new organization are themselves members of the American Mathematical Society. This older organization is itself bound by its constitution to promote the interests of mathematics in this country. That there should be any conflict between the two organizations would defeat the ends of both, and would not give the maximum service which can be rendered to American mathematicians. The American Mathematical Society has chosen, through the action of its Council, to restrict its activities to the field of pure research in mathematics, and to the promotion of those phases of mathematics which are commonly associated with that word. Those responsible for the new organization are by no means at variance with this determination, and it is their aim to carry out in good faith the separation of fields of activity provided for by the action just mentioned. This one limitation to the activities of the Association should therefore be mentioned prominently. Another restriction which is imposed, not by any agreement but by the dictates of good judgment, is that matters dealing with secondary and elementary schools should be left to the organizations already in existence devoted to that field.

The first summer meeting of the Mathematical Association of America was held by invitation at the Massachusetts Institute of Technology in Cambridge, Mass., on Friday and Saturday, September 1, 2, 1916. There were 126 persons in attendance at the various sessions ... The Association was honoured in being the first scientific body invited to meet in the new buildings of the Massachusetts Institute of Technology. This privilege was keenly appreciated and the opportunity offered to inspect these magnificent buildings embraced by many members. ... The dinner on Friday evening at the University Club in Boston was attended by eighty-one persons and was followed by a number of short addresses voicing the felicitations which were evidently in the minds of all with respect to the remarkable progress made by the new Association during the eight months of its history. ... An interesting feature at the dinner was the reading of the following cable-gram from Professor Mittag-Leffler, dated Stockholm, Sweden, August 29, 1916: "Scandinavian mathematicians assembled at Stockholm send fraternal greetings to their American brother mathematicians." In reply, Secretary Cairns was authorized to send the following message: "Members of the Mathematical Association of America reciprocate the hearty greetings of the Scandinavian mathematicians."

Note: This is Hedrick's retiring residential Address delivered at the second summer meeting of the Mathematical Association of America, at Cleveland, Ohio, on 6 September 1917.

Several circumstances combine to render peculiarly fitting a consideration at this time of the significance of mathematics. Of late we have heard much from real or alleged educators, tending to show a lack of appreciation on their part, if not on the part of the public, of the vital role which mathematics plays in the affairs of humanity. These attacks were beginning to receive some hearing in the educational world, on account of their reiteration and their vehemence, if not through intrinsic merit. A counter influence of tremendous public force, whose import is as yet seen only by those most nearly interested, has now arisen through the existence of war and the necessities of war. To the layman, lately told by pedagogical orators that mathematics lacks useful applications, the evident need of mathematical training on every hand now comes as a distinct surprise. ... by reorganizing our own instruction under the auspices of this Association, and by the recognition and encouragement of workers in the various fields of applied mathematics, we may, and I think we should, increase the appreciation of the significance of mathematics among our students, among the public, and even among ourselves. Incidentally we shall have done a service, not only to the public, in the increased emphasis upon phases of mathematics of real public service, but also to the advancement of mathematics itself, in that a better insight into the significance of mathematics will prevent or nullify mistaken attacks on the subject as one of little public worth. Such to my mind should be one function, if not the chief function, of this Association: the regeneration of a significant mathematics, the encouragement of workers in applied mathematics, and the effort to obtain recognition of the true public worth of mathematics in every phase.

Note: This address was prepared for a presentation on radio, 4 February 1933.

It is usual to emphasize the value of mathematics as a training for the whole mind, and to dwell upon the beauties and satisfactions that can be derived from the perfection of its logical proofs and from the grandeur of its higher concepts. It is also commonly known and commonly emphasized that a training in mathematics is essential for serious pursuit of engineering, of any of the physical sciences, or for some other highly technical pursuits. The history of the development of mathematics is in itself an interest to many, and it shows clearly the way in which the race has gradually conquered the physical and the quantitative problems which have arisen throughout history. For the greater part of my time today, I am to speak to you regarding the broader phases of the usefulness of mathematical training to the whole public. ... Modern civilization has become more and more involved with quantities and with relations between quantities. Computation has replaced conjecture, in business as well as in engineering; in insurance as well as in physics; in economics as well as in astronomy; in the arts of war (artillery, airplanes, maps) and in the arts of peace (automobiles, bond-issues, business forecasts). Quantities now enter in the lives of all active people, in the businesses that they conduct, and in the public questions which require legislation, on which all the voters must record public opinion.

Note: Hedrick wrote this following the announcement of a new journal, the Journal of Applied Mathematics, which would appear quarterly forming an annual volume of 300-400 pages beginning from January 1943.

Not only must applied mathematics serve the war effort, as it is now doing in increasing measure, but, looking ahead to the post-war period, it appears essential that America should be strong in the whole field of Science in order that it serve as a world centre for advanced instruction and research. The new Journal of Applied Mathematics will aid in bringing America to the forefront in applied mechanics and in other branches of applied mathematics. It is hoped that many mathematicians will approve and will give this project both moral and financial support.

Note: Hedrick wrote this piece to mark the retirement of William DeWeese Cairns who had served as Secretary-Treasurer of the Mathematical Association of America from its founding. Cairns was, at this time, elected President of the Association.

Twenty-seven years have now passed since the Mathematical Association of America was founded. During this time its membership has increased to considerably more than twice the eleven hundred charter members; meetings are held in twenty-two different sections throughout the country; and an ambitious program of periodical and book publication, and of sponsorship of other periodicals and of prize competitions, has come to fruition.