RECENT MATHEMATICAL ACTIVITIES 459 



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 complete- 

 ness 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 ele- 

 ment 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." 1 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 under- 

 takings is the cooperation which it implies. This is especially true as 

 regards a subject like mathematics, where the certainty and the perma- 

 nence of conclusions tend to inspire unusual self-reliance and indepen- 

 dence. The fact that the directors of these encyclopedias have secured 

 the cooperation of nearly three hundred mathematicians of various na- 

 tionalities implies that in this field also there is substantial evidence of 

 organized effort on a large scale. It is of interest to observe that Amer- 

 ican mathematicians are fairly well represented among these collab- 

 orators. 



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 "Inter- 

 national Commission on the Teaching of Mathematics." This com- 

 mission was created during the sessions of the fourth International 

 Congress of Mathematicians, which was. held at Borne in April, 1908, 

 and has for its main object a study of the methods and plans of mathe- 

 matical instruction in different nations. At first it was intended that 

 the commission should confine its work to secondary mathematics, but 



i E. B. Wilson, Bulletin of the American Mathematical Society, Vol. 18 

 (1911-12), p. 465. 



