December 22, 1911] 



SCIENCE 



857 



lowship and scholarship holders are fea- 

 tures of American education which, it is to 

 be hoped, will gradually pass away." They 

 are closely related to the presence in grad- 

 viate schools of large numbers of students 

 of mathematics who have reached an age 

 when their students days should be over. 

 It can not be too strongly urged on all who 

 give young men advice or who are influen- 

 tial, by awarding scholarships or otherwise, 

 in shaping their careers that it is only in 

 his first youth (not at the age of thirty or 

 thirty-five) that the foundation of real suc- 

 cess can be laid by the student of mathe- 

 matics. 



A somewhat different class is formed by 

 school teachers in active service who are at 

 the same time enrolled as graduate stu- 

 dents of mathematics, but at any moment 

 take necessarily only a small amount of 

 work. The ambition of these teachers to 

 improve their professional equipment is 

 most laudable. When, however, as is some- 

 times the case, they form a considerable 

 proportion of the enrollment of a graduate 

 school, they may be a source of weakness 

 to that school in spite of their earnestness 

 of purpose. 



The period spent by a student in gradu- 

 ate study varies from one to three, or even 

 more years; and the amount of migration 

 from one university to another does not 

 seem to be large, although the great ma- 

 jority of students attend a graduate school 

 at a different university from that at which 

 their undergraduate years were spent. 



We note also that in graduate work co- 

 education is the almost universal rule, not 

 only in the great state and other western 

 institutions where coeducation forms an 

 integral part of the scheme of education 



" Nothing in any way resembling this free award 

 of financial aid is found necessary to induce strong 

 men to attend schools of law or engineering. Cf. 

 the closing lines of this section. 



from top to bottom, but even in the most 

 conservative institutions of the east, which 

 do not admit women to their undergradu- 

 ate departments. Apart from Princeton 

 and the University of Virginia, where no 

 women are admitted, it is only in women's 

 colleges (Bryn Mawr, Vassar, etc.) and in 

 some institutions for men which have held 

 firmly to the undergraduate idea, so that 

 the amount of graduate work is very lim- 

 ited, that one sex alone will be found. 



A striking and significant fact is that 

 nearly half of all graduate students of 

 mathematics come from small colleges. 

 This is probably due to the fact that in 

 such colleges students always have the op- 

 portunity to study the elements of mathe- 

 matics and often something beyond the 

 elements, while the inducements for them 

 to turn away into other fields are slight in 

 comparison to those offered at larger insti- 

 tutions where a richer elective system pre- 

 vails. The tendency so strong in our day 

 and country to regard the man of action as 

 being of nobler clay than the man of 

 thought and ideas, reinforced by the much 

 greater financial prizes open to the former, 

 whether he be lawyer, business man or 

 engineer, creates a situation where it is not 

 easy to secure for mathematical study a 

 due proportion of the strongest youth in 

 our college communities. 



III. THE ORGANIZATION OP ADVANCED 

 MATHEMATICAL INSTRUCTION' 



The purpose of mathematical instruction 

 should be fourfold: 



I. To impart knowledge. 



II. To develop power and individual in- 

 itiative. 



III. To lead the student to express ade- 

 quately and clearly what he knows. 



' Cf. also the report of subcommittee 1. 



