Septembeb 4, 190S] 



SCIENCE 



295 



ties put in proper form to have their values 

 calculated. 



(c) The interpretation of the result, 

 which involves a translation of the same 

 from the mathematical language in which 

 it has been obtained into the original 

 language of the problem and a discussion 

 of the practical bearings of the same. 



In conversation with a fellow mathe- 

 matician at this meeting he surprised me 

 by saying that he expected a problem to 

 be put into mathematical language before 

 it was submitted to him and I presume he 

 did not feel bound to interpret his results. 

 Now if "pure mathematicians" regard 

 practical problems in this way, engineers 

 and other practical men have just cause 

 for finding fault with "pure mathe- 

 matics," and to teach mathematics in this 

 way is to render it valueless to most stu- 

 dents. Personally I should refuse to 

 undertake a problem unless I made the 

 analysis and interpretation as well as the 

 solution. 



In many if not in most problems the 

 analysis and interpretation are the main 

 parts. They require a broad knowledge of 

 practical conditions and of other sciences 

 and are far more interesting than the mere 

 solution, especially as they often bring into 

 play a large amount of ingenuity and in- 

 vention, as well as imagination and judg- 

 ment. A mathematician who can not 

 make the analysis and interpretation of a 

 problem is not to be trusted with the solu- 

 tion and an engineer who is fully compe- 

 tent to make them had better undertake 

 the solution himself or put the whole prob- 

 lem into the hands of a mathematician 

 fully competent to undertake it. 



There is no excuse for a "pure mathe- 

 matician" remaining ignorant of the prac- 

 tical side of the problems he teaches, and 

 his mathematics will not be interesting or 

 trustworthy. Let him cultivate the ac- 

 quaintance of the truly educated engineer. 



who will be only too glad to discuss prob- 

 lems with him and give him all the prac- 

 tical information he needs. But there are 

 too many engineers who are not truly edu- 

 cated and who know less about mathe- 

 matics than the "pure mathematician" 

 does about practical things, and they ought 

 to cultivate the acquaintance of the mathe- 

 matician and rub off the worst parts of 

 their ignorance before they attempt to 

 criticize the teaching of mathematics. But 

 it is much easier to find fault and say that 

 they never found any use for such and 

 such mathematical branches, when they 

 never gave them enough attention to make 

 them of any use. 



Every mathematical teacher should teach 

 all three parts of a problem, but the aver- 

 age engineering student is so indifferent to 

 real progress and his limited time is so 

 taken up with other things that he may get 

 through his course knowing very little 

 about mathematics, no matter how well it 

 may be taught. 



Students with fair ability that really 

 want to learn a particular subject can do 

 it even under indifferent teachers, but un- 

 less students exert themselves to learn, the 

 best teacher can not put knowledge into 

 them. Discuss the subject to the limit, 

 analyze and adjust the engineering courses 

 to a nicety, write new text-books, adopt 

 new systems and get new teachers and the 

 thing will remain about as it is; teachers 

 will teach and students will expect them 

 to, while only a few will learn, whether 

 the teacher expects them to or not. 



By H. T. Eddy, Dean of the Graduate 



School and Professor of Mathematics 



and Mechanics, College of Engineering, 



University of Minnesota. 



Complaint has been made that in our 



teaching of mathematics we do not pay due 



attention to psychological and pedagogical 



principles. I want to consider for a mo- 



