444 



SCIENCE 



[N. S. Vol. XLI. No. 1056 



knowledge of mathematical problems and proc- 

 esses without becoming a mathematician. 



This is a large matter, involving all the 

 cardinal divisions of knowledge. I have 

 neither time nor competence to deal with 

 it fully or explicitly in all its bearings. As 

 indicated by the title of this address it is 

 my intention to confine myself, not indeed 

 exclusively but in the main, to consideration 

 of the question in its relation to advanced 

 instruction in mathematics. The obvious 

 advantages of this restriction will not, I 

 believe, be counterbalanced by equal dis- 

 advantages. For, much as the principal 

 subjects of university instruction differ 

 among themselves, it is yet true that as 

 instruments of education they have a com- 

 mon character and for their efficacy as 

 such depend fundamentally upon the same 

 educational principles. A discussion, there- 

 fore, of an important and representative 

 part of the general question will naturally 

 derive no little of whatever interest and 

 value it may have from its implicit bearing 

 upon the whole. It is not indeed my inten- 

 tion to depend solely upon such implicit 

 bearings nor upon the representative char- 

 acter of mathematics to intimate my opin- 

 ion respecting the question in its relation to 

 other subjects. On the contrary, I am going 

 to assume that specialists in other fields 

 win allow me, as a lay neighbor fairly in- 

 clined to minding his own affairs, the priv- 

 ilege of some quite explicit preliminary 

 remarks upon the larger question. 



I suspect that my interest in the matter 

 is in a measure temperamental; and my 

 conviction in the premises, though it is not, 

 I believe, an unreasoned one, may be some- 

 what colored by inborn predilection. At 

 all events I own that a good many years of 

 devotion to one field of knowledge has not 

 destroyed in me a certain fondness for 

 avocational studies, for boolis that deal with 

 large subjects in large ways, and for men 

 who, uniting the generalist with the spe- 



cialist in a single gigantic personality, can 

 show you perspectives, contours and reliefs, 

 a great subject or a great doctrine in its 

 principal aspects, in its continental bear- 

 ings, without first compelling you to survey 

 it pebble by pebble and inch by inch. I 

 can not remember the time when it did not 

 seem to me to be the very first obligation 

 of universities to cherish instruction of the 

 kind that is given and received in the avo- 

 cational as distinguished from the voca- 

 tional spirit — the kind of instruction that 

 has for its aim, not action but understand- 

 ing, not utilities but ideas, not efficiency 

 but enlightenment, not prosperity but 

 magnanimity. For without intelligence 

 and magnanimity — without light and soul — 

 no form of being can be noble and every 

 species of conduct is but a kind of blunder- 

 ing in the night. I could hardly say more 

 explicitly that I agree heartily and entirely 

 with the main contention of President 

 Butler's pronouncement. Indeed I should 

 go a step further than he has gone. He 

 has said that a university department is 

 not well organized and is not doing its 

 duty until it establishes and maintains the 

 kind of instruction I have tried to char- 

 acterize. To that statement I venture to 

 add explicitly — what is of course implicit 

 in it — that a university is not well organ- 

 ized and is not doing its duty until it makes 

 provision whereby the various departments 

 are enabled to foster the kind of instruction 

 we are talking about. That in all major 

 subjects of university instruction there 

 ought to be given courses designed for stu- 

 dents of "maturity and power" who, whilst 

 specializing in one subject or one field, de- 

 sire to generalize in others, appears to me 

 to be from every point of view so reasonable 

 and just a proposition that it would not 

 occur to me to regard it as questionable or 

 debatable were it not for the fact that it 

 actually is questioned and debated by 

 teachers of eminence and authority. 



