52 UNIVERSITY OF MISSOURI BULLETIN 



all possible popular explanation, though they do directly affect 

 some practical problems like those of physics and engineer- 

 ing, which are of immediate use to the race. 



I may pass perhaps briefly in review one great phase 

 of mathematical activity at present which can be explained 

 properly, namely, the activity exhibited toward reform in 

 mathematical teaching. Societies have been created, not only 

 in this country, but in every civilized nation, for the study 

 of methods of teaching and improvement of subject-matter 

 taught. The actual results are a radical change in the mathe- 

 matics taught in secondary and primary schools, and a radical 

 change also in the knowledge necessary on the part of the 

 teacher. Among the most prominent activities at present are 

 those of the American Federation of Teachers of Mathematics 

 and Science, a national organization in this country, and the 

 similar activities of an International Commission on the 

 Teaching of Mathematics recently created by the Interna- 

 tional Congress of Mathematicians at Rome, which in con- 

 junction with the national commissions of every civilized 

 nation is soon to make a voluminous and exhaustive mathe- 

 matical report on the present status of mathematical teaching 

 of all classes, with recommendations concerning the future. 

 The National Commission for the United States has asked 

 the assistance of mathematicians throughout the country, both 

 in colleges and in secondary schools, and the importance of 

 this work for the United States alone will certainly be tre- 

 mendous. 



Along the lines of scientific research I can indicate but 

 little, for the reasons which I have previously mentioned, 

 since mathematics today has passed the point of hasty under- 

 standing by him who runs. Briefly, the main fields of func- 

 tion theory, geometry, the theory of limits are pressing for- 

 ward as never before. A new and radically successful attack 

 has been made upon the philosophy of mathematics and upon 

 the foundations of this and other sciences. It is perhaps more 



