856 



SCIENCE 



[N. S. Vol. XXXIV. No. 



Johns Hopkins, advanced instruction was 

 at once placed in a department by itself, in 

 by far the larger number of institutions it 

 developed very gradually within the old 

 college, room being made for it by the 

 elective system; and it was only slowly, 

 even in the larger institutions, that small 

 groups of graduate students began to col- 

 lect. The somewhat unorganized condi- 

 tion, which was then the rule, is still to be 

 found in the weaker institutions of the 

 country and also in some colleges which in 

 their chosen field of undergraduate work 

 are strong, but which voluntarily renounce 

 any substantial development of graduate 

 instruction. The great universities, how- 

 ever, have all, since the year 1890, devel- 

 oped well-organized graduate schools fre- 

 quented by the graduates of their own and 

 other colleges. It may be added, to avoid 

 possible misconception, that the graduate 

 schools which sprang full-fledged into ex- 

 istence and those which developed slowly 

 from the old college no longer form two 

 distinct classes. Some of the strongest 

 graduate schools in the country are now to 

 be found among the last-named institu- 

 tions. 



In contrast with such countries as 

 France, Italy and, to a less extent, Ger- 

 many, we note the complete lack of central 

 control or organization in the United 

 States. Many variations are hereby made 

 possible which are, for a country like ours, 

 almost a necessity ; and competition, on the 

 whole healthy, springs up between the dif- 

 ferent institutions. 



In conclusion we note that of late years 

 some technological schools (for instance the 

 Massachusetts Institute of Technology) 

 have undertaken a limited amount of 

 graduate instruction in mathematics. As 

 this instruction does not differ, except in 

 the greater emphasis laid on applied math- 



ematics, from that given at colleges and 

 universities, and since the amount of such 

 instruction at technological institutons is 

 as yet very small in comparison to the 

 whole amount of mathematical graduate 

 instruction in the cotmtry, we have not 

 thought it necessary to mention these tech- 

 nological schools specifically in what fol- 

 lows. 



II. THE GRADUATE STITDENT OF MATHE- 

 MATICS AT THE PRESENT DAY 



Owing to the great variety of standards 

 for the bachelor's degree in the different 

 colleges of the country, the students of a 

 single graduate school enter it with very 

 diverse preparation. This is, however, not 

 so disturbing as might be expected, owing 

 to the fact that at every university in 

 which a graduate school exists there is a 

 collegiate or undergraduate department 

 whose instruction is freely open to the 

 graduate student who is in need of it. We 

 may then say that not all work done by 

 graduate students is graduate work. On 

 the other hand, the ambitious and capable 

 senior in colleges allowing considerable 

 freedom of election will frequently be do- 

 ing work of a distinctly graduate character 

 in the same classes with able graduates of 

 colleges in good standing. 



If we thus miss any sharp line of de- 

 marcation at the lower limit of the gradu- 

 ate school between graduates and under- 

 graduates, we find a similar phenomenon 

 at the upper limit where the graduate stu- 

 dent often passes by almost imperceptible 

 steps into the teacher. Indeed there are 

 graduate schools, even among the better 

 institutions of the country, the bulk of 

 whose students are at the same time as- 

 sistants or instructors. This, and the very 

 high percentage of graduate students of 

 mathematics the country over who are fel- 



