Page:Popular Science Monthly Volume 85.djvu/463

Rh make twenty large volumes, each containing about five hundred pages.

While this work may appear extensive for an encyclopedia which aims to give in a concise form the fully established mathematical results, yet the French edition promises to become still more extensive. The first part of this edition appeared in August, 1904, and the aggregate of the published parts is at present only about one half as large as that of the German edition. On the other hand, most of the subjects which have been treated in both editions are treated with much more completeness in the French than in the German edition, as might be expected from the fact that the former edition is, in the main, based on the latter. According to the latest announcements some parts of the German edition are to be based on parts which have already appeared in the French edition.

The magnitude of these undertakings is certainly not the main element of interest to the educated man. In fact, the question has been raised whether these encyclopedias are not becoming too large to fulfil one of the main objects in view; viz., to provide a work by means of which the student can determine quickly what has been done along various lines in the mathematical sciences. A keen observer recently made the following significant remark, "the whole encyclopedia, whether German or French edition, seems of late to have run riotously and fruitlessly to leaves." In this connection it may be observed that a big and vigorous tree has normally more leaves than a little one.

One of the main elements of interest in such big educational undertakings is the cooperation which it implies. This is especially true as regards a subject like mathematics, where the certainty and the permanence of conclusions tend to inspire unusual self-reliance and independence. The fact that the directors of these encyclopedias have secured the cooperation of nearly three hundred mathematicians of various nationalities implies that in this field also there is substantial evidence of organized effort on a large scale. It is of interest to observe that American mathematicians are fairly well represented among these collaborators.

A big current mathematical undertaking which affects directly a much larger number of people than the encyclopedias mentioned above is the work which is being done under the direction of the "International Commission on the Teaching of Mathematics." This commission was created during the sessions of the fourth International Congress of Mathematicians, which was held at Rome in April, 1908, and has for its main object a study of the methods and plans of mathematical instruction in different nations. At first it was intended that the commission should confine its work to secondary mathematics, but