446 



SCIENCE 



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



Where is the university professor to whom 

 such students have not revealed themselves 

 as such in conversation? Who is it that 

 has not learned of their existence through 

 the testimony of others? No doubt some 

 of us not only have known students of the 

 kind, but have tried in a measure to serve 

 them. We may as well be frank. I have 

 myself for some years oifered in my subject 

 a course designed in large part for students 

 having no vocational interest in mathe- 

 matics. I may be permitted to say, for 

 what the testimony may be worth, that the 

 response has been good. The attendance 

 has been composed about equally of stu- 

 dents who were not looking forward to a 

 career in mathematics and of students who 

 were. And this leads me to say, in passing, 

 that, if the latter students were asked to 

 explain what value such instruction could 

 have for them, they would probably answer 

 that it served to give them some knowl- 

 edge ahout a great subject which they could 

 hardly hope to acquire from courses de- 

 signed solely to give knowledge of the 

 subject. Every one knows that it often 

 is of great advantage to treat a subject as 

 an object. One of the chief values of 

 w-dimensional geometry is that it enables 

 us to contemplate ordinary space from the 

 outside, as even those who have but little 

 imagination can contemplate a plane be- 

 cause it does not immerse them. Return- 

 ing from this digression, permit me to 

 ask : if, without trying to discover the type 

 of student in question, we yet become 

 aware, quite casually, that the type actu- 

 ally exists, is it not legitimate to infer that 

 it is much more numerously represented 

 than is commonly supposed? And if such 

 students occasionally make their presence 

 known even when we do not offer them 

 the kind of instruction to render their 

 wants articulate, is it not reasonable to 

 infer that the provision of such instruction 



would have the effect of revealing them in 

 much greater numbers? 



Indeed it does not seem unreasonable to 

 suppose that a "strong substantial course" 

 of the kind in question, in whatever great 

 subject it were given, would be attended 

 not only by considerable numbers of reg- 

 ular students but in a measure also by 

 officers of instruction in other subjects 

 and even perhaps by other qualified resi- 

 dents of an academic community. Only 

 the other day one of my mathematical 

 colleagues said to me that he would rejoice 

 in an opportunity to attend such a course 

 in physics. The dean of a great school of 

 law not long ago expressed the wish that 

 some one might write a book on mathe- 

 matics in such a way as would enable stu- 

 dents like himself to learn something of 

 the innerness of this science, something of 

 its spirit, its range, its ways, achievements 

 and aspiration. I have known an eminent 

 professor of economics to join a beginners' 

 class in analytical geometry. Very recently 

 one of the major prophets of philosophy 

 declared it to be his intention to suspend 

 for a season his own special activity in 

 order to devote himself to acquiring some 

 knowledge of modern mathematics. Simi- 

 lar instances abound and might be cited 

 by any one not only at great length, but in 

 connection with every cardinal division of 

 knowledge. Their significance is plain. 

 They are but additional tokens of the fact 

 that the race of catholic-minded men has 

 not been extinguished by the reigning spe- 

 cialism of the time, but that among students 

 and scholars there are still to be found 

 those whose curiosity and intellectual in- 

 terests surpass all professional limits and 

 crave instruction more generic in kind, 

 more liberal, if you please, and ampler in 

 its scope, than our vocationalized programs 

 afford. 



As to the question of values, I maintain 



