July 31, 1908] 



SCIENCE 



133 



struetor on instruments, but a poor teacher 

 of civil engineering. 



After all, it is not so much abstract 

 courses as it is personal men with which we 

 have to do, it is not mere knowledge of 

 facts or facility in mathematical manipula- 

 tion, but it is training. The young man 

 is to be developed, his native individuality 

 is to be the basis, he is to increase not only 

 his knowledge, but his powers and the 

 ability to use them. It is not mathematical 

 skill so much as a mathematical sense, or 

 mathematical common-sense, which is 

 wanted. With pure mathematics as a sci- 

 ence we have no quarrel — and little affilia- 

 tion. 



If you ask men who use engineering 

 graduates what qualities they should pos- 

 sess, you will find that special prominence 

 is given to "common-sense" and "the 

 ability to do things." In mathematical 

 training it is quality rather than quantity 

 which is of first consequence. It should 

 develop the facility for systematic and 

 logical reasoning, thus furnishing a general 

 method as well as a specific means of 

 getting results. 



We are concerned with applied mathe- 

 matics. The ability to state a problem ; to 

 recognize the elements which enter into it ; 

 to see the whole problem without over- 

 looking some important factor ; to use good 

 judgment as to the reliability or accuracy 

 of the data or measurements which are in- 

 volved ; and, on the other hand, the ability 

 to interpret the result; to recognize its 

 physical significance; to get a common- 

 sense perspective view of its meaning and 

 the consequences which may follow; to 

 note the bearing of the various data upon 

 the final result ; to determine what changes 

 in original conditions may change a bad 

 result into one which is practical and effi- 

 cient—such abilities as these are of a 

 higher order than the ability to take a 

 stated problem and work out the answer. 



It may be urged that all this is not strictly 

 mathematics. But it is just this sort of 

 judgment and insight which makes mathe- 

 matics really useful, and without them 

 there is danger that they may be neither 

 safe nor sane. 



The trend in education is to a closer re- 

 lation to the affairs of life. Science and 

 applied science, scientific and engineering 

 laboratories, are overcoming old ideas and 

 prejudices. Modern engineering develop- 

 ment brings its transforming influence to 

 bear upon education as well as the utilities 

 of modern life. The engineering school 

 has had a phenomenal growth within the 

 lifetime of the recent graduate— a growth 

 in ideals and methods as well as students 

 and equipment. It has raised and agitated 

 broad questions as to what constitutes 

 efficient education for producing effective 

 men. It has aimed to combine not only 

 the abstract with the concrete, the lecture 

 room with the laboratory, and the scientific 

 experiment with the practical test; but it 

 has sought by various means to bring the 

 work of the school into close relation with 

 active professional and commercial prac- 

 tise. It has a definiteness of aim and pur- 

 pose which other educational courses are 

 apt to lack. It sets out to produce men 

 who can deal with forces and materials 

 according to scientific principles. It de- 

 velops men whose contact with physical 

 facts and natural laws at first hand and 

 whose ability to reason logically fit them 

 for dealing with new problems. The 

 training which fits men for handling engi- 

 neering problems is the kind that is needed 

 for dealing with the organization and di- 

 recting of men. The sphere of the engi- 

 neer is one the scope of which will con- 

 tinue to increase as engineering education 

 and training produce men whose contact 

 with natural phenomena gives them an in- 

 herent respect for facts as their premises, 

 who are able to think straight to logical 



