August 28, 1908] 



SCIENCE 



261 



believe that in teaching the subject to engi- 

 neering students the best results would be 

 obtained if the teachers were engineers, or 

 at least if they were near enough to being 

 engineers to take an interest in the con- 

 crete problems themselves as distinct from 

 their solution. If I am correct in the be- 

 lief that mathematics should be taught as a 

 tool, then it can be taught best by those 

 who know how to use it as a tool. Un- 

 fortunately, however, it is difficult to get 

 engineers who are sufficiently interested in 

 mathematics and sufficiently masters of 

 that subject, who are willing to devote 

 themselves to teaching. The men who are 

 interested in the problems prefer to devote 

 themselves to those problems, and to go 

 into practical work. It is not necessary, 

 however, as suggested above, that the 

 teachers of mathematics should be engi- 

 neers if only they will take an interest in 

 the problems themselves, and in the point 

 of view which the student should take. 

 They can do this by cooperation with the 

 engineering teachers, by attending engi- 

 neering courses, and, perhaps, by a little 

 more realization than they now have that 

 their work is preliminary to other and 

 more important work, and that as a matter 

 of fact if the engineering student does not 

 learn to use his mathematics as a tool it 

 is practically of no value to him. For the 

 engineer, mathematics is the servant, and 

 the mathematical teacher should aim to 

 teach the subject in such a way as to obtain 

 as nearly as possible the results which in- 

 telligent engineering teachers and practi- 

 tioners desire to have obtained. 



George P. Swain 

 Massachusetts Institute of Technology 



from the standpoint of the professor of 

 mathematics in the engineering 



COLLEGE 



We must not take too seriously what 

 engineers have to say in an educational 



discussion, nor take too much to heart their 

 views on the mathematical curriculum. 

 Practising engineers are not in the habit 

 of thinking very continuously on any edu- 

 cational question, although, of course, they 

 must not confess inability to respond when 

 they are called upon for pedagogical opin- 

 ions. Every practitioner in the law would 

 doubtless express views concerning legal 

 education if summoned to do so, but he 

 would be a rash educator who would at- 

 tempt to follow their advice without much 

 circumspection. I, myself, prefer to judge 

 of the engineer's views upon educational 

 matters by studying his actions rather than 

 his words. The things engineers "do" 

 may be taken as a true expression of their 

 deliberate judgment— what they "say" is 

 often ill thought out and in contradiction 

 to their deeds. I therefore prefer to judge 

 of the present needs in the mathematical 

 instruction for engineers by the actual 

 tendencies that I observe in the evolution 

 of technology itself. 



What are the great changes that the 

 engineering profession has made in tech- 

 nical science in this country in the last 

 quarter of a century? The changes are 

 quite obvious and not difficult to state. In 

 former days engineering technology was 

 founded chiefly upon current practise 

 rather than upon established principles; it 

 was more closely allied to the crafts than 

 to science. Not only is that day past, but 

 it is no longer the ease that technical sci- 

 ence looks entirely to pure science for its 

 fundamental material. It has so grown 

 that it is investigating for itself and, in 

 greater and greater measure, developing 

 the basal principles for its own needs. 

 There are very few American treatises in 

 pure science which will compare in scien- 

 tific thoroughness with several treatises 

 which have lately issued from the engineer- 

 ing press. This is a very hopeful sign in 

 the growth of knowledge— to see applied 



