December 22, 1911] 



SCIENCE 



861 



cision that all other students of mathe- 

 matics in graduate schools become in- 

 structors in mathematics in colleges or 

 universities. The condition of twenty-five 

 years ago, where college instructors in 

 mathematics were taken from among the 

 freshly graduated students of a college 

 (usually the same college where they were 

 to teach), has now become the exception 

 instead of the rule; and where it still oc- 

 curs, the appointment is usually a tempo- 

 rary one, both the instructor and the col- 

 lege expecting that, after a year or two of 

 teaching, further graduate study will fol- 

 low. The gain involved in this changed 

 state of affairs, both in breadth of view 

 and in real mastery of the subject, the 

 teaching of which is to be the young man's 

 life work, is so obvious as to require no 

 further comment here. If the student can 

 furthermore be given some comprehension 

 of the fact that the science of mathematics is 

 a living and growing one through contact 

 with other students or instructors who are 

 themselves contributing to this growth, 

 and still more if he himself can take some 

 part in the development of mathematical 

 knowledge, his outlook on mathematics in 

 particular and intellectual life in general 

 will have been so broadened that he can 

 hardly fail to become a better member of a 

 college faculty than would otherwise have 

 been the case. 



After all this has been said, we must, 

 however, admit that this question has also 

 another side less pleasant to contemplate. 

 What passes for original research, in this 

 country more even than abroad, is often 

 hardly a real contribution to mathematical 

 progress at all, but merely a grinding out 

 of results, which if they have only never 

 been published before may be as unimpor- 

 tant and unattractive as you please; they 

 form an "original contribution." One is 

 tempted to answer, Yes, in the same sense 



as the brass button in the contribution box. 

 We may feel certain that in the long run 

 this will be the character of the research 

 work done by students who have no real 

 capacity or inclination for original work, 

 but who are pushed into it by the increas- 

 ing demand, on the part of certain heads of 

 departments, for the doctor's degree as a 

 necessary preliminary to college teaching. 

 The pressure thus produced will surely, if 

 persisted in, bring forth an increasing 

 yearly crop of doctors — ^success can be ob- 

 tained by almost any one with a fair mathe- 

 matical capacity and with sufficient indus- 

 try and patience, either by going abroad 

 or by going to one of the weaker American 

 institutions with an ambition for giving the 

 doctor's degree. It is doubtful if the time 

 will ever come, certainly it will not come 

 for a great many years, when all the mem- 

 bers of the teaching staffs of the large uni- 

 versities of the country, and the colleges of 

 like rank, can be men with a real capacity 

 for original investigation; the number of 

 all such men in the country falls far short 

 of (one might almost say that it is of a 

 different order of magnitude from) the 

 number of places to be filled. 



The pseudo doctor, to whom reference 

 was made above, is often narrowed rather 

 than broadened by the bit of investigation 

 which he has been set to do, and becomes 

 thereby less effective as a teacher, investi- 

 gation for him becoming a fetich for which 

 he forgets all other ideals. Or, on the 

 other hand, he may let all thought of orig- 

 inal work drop out of his mind when once 

 he has secured his degree. In either case 

 the letters he places after his name ought 

 not to go very far in recommending him 

 for teaching positions. A broad and deep 

 mathematical training should surely be de- 

 manded by all the institutions of the coun- 

 try which claim collegiate rank as a pre- 

 requisite for a permanent appointment on 



