MATHEMATICAL INSTRUCTION 163 



which can scarcely be attained in any other way, yet the early attack 

 on research problems has not been free from undesirable results. If 

 the mind is centered on one line of thought it is less apt to be in condi- 

 tion to receive deep impressions of other fields which may be equally 

 important. Only the greatest minds have been able to attain to those 

 broad and impressive views which comprehend the true correlation of 

 the different lines of mathematical activity, in addition to making im- 

 portant contributions along any one line. In recent years there has 

 been a tendency to encourage breadth of scholarship even at the expense 

 of research in early years, — a tendency which Klein has aptly named 

 encyclopedic. 4 



In American mathematical research activity was very limited until 

 recent years. Within the last decade the mathematical productivity 

 has more than doubled, both as to quality and as to quantity. This 

 has been largely due to foreign training, as only very few of our larger 

 institutions have a sufficient number of research men on their faculties 

 to afford their students opportunities to enter upon fields of research 

 which are best suited to their tastes and ability. Hence the encyclo- 

 pedic tendency of German mathematics, and possibly also of that of 

 France, should not affect us for a number of years. 



The tendencies which have been mentioned relate principally to 

 university instruction. During the last few years there has been an 

 unprecedented activity along lines which relate principally to secondary 

 schools. This movement is sometimes called the Perry movement, 

 in view of the great activity of Professor John Perry, of the Eoyal 

 College of Science, London. Perry's paper at the recent Glasgow 

 meeting of the British Association for the Advancement of Science 

 provoked a great deal of discussion, and was followed by the appoint- 

 ment of a committee with Professor Forsyth, of Cambridge, as chair- 

 man, ' to report upon improvements that might be effected in the 

 teaching of mathematics, in the first instance in the teaching of ele- 

 mentary mathematics, and upon such means as they think likely to 

 effect such improvements.' 



In our own country the movement has been brought into prom- 

 inence largely through the efforts of Professor Moore, who devoted a 

 part of his presidential address before the American Mathematical 

 Society to questions related to this movement. That the time was 

 ripe for such a movement seems evidenced by the numerous organiza- 

 tions of teachers of mathematics with a view to the discussion of ques- 

 tions related to the improvements in teaching and in the selection of 

 subject matter. 5 



* Klein, Jahresbericht der Deutschen Mathematiker-Vereinigung, Vol. 13 

 (1904), p. 473. 



6 The following associations have been organized within a few years: 



