862 



SCIENCE 



[N. S. Vol. XXXIV. No. 888 



their teaching staff. They will naturally 

 demand also some ability as a teacher. If 

 in addition they can secure an investigator 

 of a genuine sort, even though his caliber 

 be slight, they should usually regard them- 

 selves as fortunate, though a few of the 

 strongest institutions can and should set 

 themselves a much higher standard. On 

 the other hand, our stronger graduate 

 schools should continue, as they are now 

 doing, to encourage every capable student 

 to try his hand at some piece of original 

 investigation, but they should not hesitate, 

 after a fair trial, to tell him, if that turns 

 out to be the case, that he is not fitted for 

 that kind of work. 



No specific training for the profession of 

 college or university instructor is commonly 

 given in graduate schools apart from the 

 training in mathematics (cf. subcommittee 

 3, section V.). The statement made in sec- 

 tion III. of the present report that the 

 training in clear and adequate exposition 

 which is given to graduate students of 

 mathematics is frequently insufficient is of 

 peculiar importance in relation to the fu- 

 ture teacher. While it is probably not de- 

 sirable to attempt to train the future col- 

 lege or university instructor in the art of 

 teaching, the question whether more can 

 not be done to lead graduate students of 

 mathematics to express their ideas well 

 both in spoken and in written form is 

 worthy of serious consideration. 



Let us turn now from the graduate stu- 

 dents, who are to become college instruc- 

 tors, to the actual instructors and pro- 

 fessors of mathematics in our colleges and 

 universities. If we compare conditions at 

 the present day with those existing twenty 

 years ago, a very great increase in the 

 standard of mathematical knowledge on 

 the part of the teaching staff is evident. 

 That the improvement here has not been 



even greater is due in large measure to the 

 fact that the supply of well-trained gradu- 

 ate students falls far short of the demand. 

 Weak appointments are also made from 

 time to time, owing to ignorance on the 

 part of trustees or heads of departments of 

 what really constitutes a mathematician, 

 to the pernicious view that administrative 

 ability may be allowed to take the place 

 of mathematical ability, or to other like 

 causes. Flagrant cases of this kind oc- 

 casionally occur which make one blush for 

 the good name of American universities, 

 but such cases are now merely sporadic 

 and one gains comfort by contemplating 

 conditions in Germany only a hundred 

 years ago. "What is needed here, as in so 

 many other places in American life, is a 

 strengthening of intelligent idealism (we 

 have more than enough misdirected ideal- 

 ism amongst us) based upon knowledge, 

 and there seems every reason to hope that 

 the great development of mathematics in 

 this countrj' during the last twenty years, 

 evident chiefly in the growth and activity 

 of the American Mathematical Society, will 

 in an ever-increasing degree supply the in- 

 telligent and influential public opinion 

 here needed. The shortage, above men- 

 tioned, in the supply of instructors in 

 mathematics forms the most serious aspect 

 of the situation. 



For various further points : The excessive 

 biirdening of young instructors with 

 drudgery, which still often occurs; inade- 

 quate salaries ; the burdening of professons 

 with administrative work; we refer to the 

 report of subcommittee 3. 



V. STUDY BY AMERICANS ABEOAD 



No account of higher mathematical edu- 

 cation in America would be complete with- 

 out a reference to the part played by the 

 study of Americans abroad. What an im- 



