266 



SCIENCE 



[N. S. Vol. XXVIII. No. 713 



are in the background, and he often fails 

 to see the possibility of using mathematical 

 principles until he is trained to do so by 

 the professor of engineering. If the pro- 

 fessor, through lack of knowledge or lack 

 of interest, avoids the use of mathematics, 

 the student will soon lose the little he has 

 learned. 



In other words, the mathematical train- 

 ing of a student is not complete when he 

 leaves the department of mathematics. It 

 is possible that better results could be ob- 

 tained if the mathematical department had 

 more time, say for a course in applications 

 of mathematics to miscellaneous problems. 

 But, as a rule, in our technical schools the 

 department of mathematics is allowed 

 barely time to teach the necessary tech- 

 nique with what illustrations and applica- 

 tions can be squeezed in. Hence the math- 

 ematical department delivers to the engi- 

 neering department an unfinished product 

 and it is the engineer's duty to teach the 

 student to use the mathematics he has 

 learned. Unfortunately, the professor of 

 engineering is too often a poor mathema- 

 tician and avoids this duty. 



One of the hardest things a student has 

 to do is to combine two different domains 

 of knowledge, each somewhat unfamiliar, 

 so that he may work freely in both at once, 

 using each as a help in the other. It is 

 this difficulty which makes analytical geom- 

 etry traditionally hard, and which the stu- 

 dent meets again when he studies any form 

 of applied mathematics. It is partly to 

 help overcome this difficulty that we have 

 just made a rearrangement of our mathe- 

 matical instruction in the Massachusetts 

 Institute of Technology. We no longer 

 have courses in algebra, analytic geometry 

 and differential and integral calculus, but 

 have combined these into one "course in 

 mathematics" extending through two 

 years. Into this course the elements of 



analytic geometry and of calculus are in- 

 troduced early and continued late. We 

 hope thus to give these principles more 

 time to become completely domiciled in the 

 student's mind. We have also been en- 

 abled to carry out two principles : the first 

 is to introduce no subject until some use 

 is to be made of it, and the second to 

 handle each problem by the method best 

 adapted to it, rather than by the methods 

 of the particular branch of mathematics 

 which one might at the moment -be study- 

 ing under the old classification. We hope 

 in this way to increase the efficiency of our 

 mathematical teaching. 



F. S. Woods 

 Massachusetts Institute of Technology 



The program shows three standpoints 

 from which discussion is to emanate. I 

 occupy no one of them. It is true I have 

 had some engineering practise, but I can 

 not be termed a practising engineer. I 

 have had charge of mathematics for engi- 

 neering students in two engineering col- 

 leges, but for nearly a decade now I have 

 not met students in mathematics; and, 

 indeed, I have taught, all told, but an insig- 

 nificant amount. I am in somewhat close 

 touch with engineering students, but they 

 belong to a particular field, namely, 

 mining, which is possibly less dependent 

 on mathematics than are other branches 

 of engineering. My view-point is, there- 

 fore, somewhat of a compromise or average 

 of the three specified in the announcement. 



The present discussion seems to me sig- 

 nificant. It may bring forth results. In 

 fact it seems to have had some immediate 

 consequences. Last evening after the din- 

 ner I heard a very clever mathematician 

 admit that he felt really humble, and I 

 heard a well-known engineer say that to 

 his great surprise some mathematicians had 

 a human side. I asked a pure mathema- 

 tician sitting near me to show me his hu- 



