Decembek 22, 1911] 



SCIENCE 



•863 



portant factor this was in introducing ad- 

 vanced mathematical instruction and re- 

 search into America has already been men- 

 tioned in section I. In the early days 

 the possibilities for advanced mathematical 

 study in this country were very limited, 

 so that it was natural that students able to 

 do so should go abroad where they could 

 find this opportunity in large measure. At 

 the present day it may safely be said that 

 at several of the stronger American gradu- 

 ate schools most American students find 

 mathematical opportunities better suited 

 to their needs than are to be found at any 

 place abroad. Nevertheless, students still 

 go abroad in apparently undiminished 

 numbers to study mathematics," and their 

 decision to do this is frequently a wise one. 

 Let us inquire how this can be the case. 

 There come first considerations of a 



" It would be a matter of considerable interest to 

 kave statistics on the number of American students 

 who go abroad each year to study mathematics and 

 the length of time they stay. Such statistics would 

 seem to be very difficult if not impossible to secure. 

 As to the proportion of instructors of graduate 

 courses in mathematics who have spent at least one 

 year abroad, see the report of subcommittee 1, 

 ieetion III. Far less important is the question of 

 the number of doctors ' degrees conferred on 

 Americans abroad. Such information might be 

 secured. We content ourselves with giving two 

 such items, for which we are indebted to Dr. Dun- 

 tarn Jackson: 



At Gottingen in the years 1889-1909, inclusive, 

 twenty-two Americans received the degree in math- 

 ematics, while no degrees in mathematics had been 

 conferred on Americans during the four previous 

 years. 



At Leipzig in the years 1885-1902, inclusive, 

 aight Americans received the degree in mathe- 

 matics, while after this time Americans seem to 

 have ceased taking the degree in mathematics 

 there. 



At present from two to four Americans take 

 their degree in mathematics in Germany each year, 

 as against an average of sixteen or seventeen in 

 the United States. 



nonmathematical character. It is desir- 

 able for every one to become acquainted at 

 first hand with other countries than his 

 own, and this is doubly true for an Ameri- 

 can, for whom a period of residence in 

 European countries is invaluable. It is 

 true that the student often seems to have 

 brought back from a year or two of resi- 

 dence abroad only a strengthening of his 

 earlier national prejudices, since the mote 

 in the neighbor's eye is so very easy to dis- 

 cern ;" but if he is worth his salt, he brings 

 with him a fund of impressions and experi- 

 ences which, as time goes on, greatly 

 enrich his life. For this reason alone 

 study abroad is to be recommended even at 

 some mathematical sacrifice. A second 

 consideration is that the cost of living in 

 Germany, to which country the great ma- 

 .jority of students going abroad have al- 

 ways resorted, even after the great increase 

 of the last few years, is still lower than in 

 America, and in particular, the tuition 

 fees are much less than in many of the 

 larger American institutions, especially of 

 the east. These facts largely counterbal- 

 ance the expense of the trip across the 

 ocean. Finally, it is to be remembered 

 that a year or two of mathematical study 

 in Germany, France or Italy gives the stu- 

 dent a reading and speaking knowledge of 

 one of the great languages of modern 

 thought, besides his own native English, 

 such as can hardly be acquired in any 

 other way. 



When we come to mathematical consid- 

 erations, the first question we must ask is 

 whether getting a degree or learning math- 

 ematics is the prime object of the student 

 going abroad. It is the former which, 



" There are also cases in which he takes so kindly 

 to foreign conditions as to become out of touch 

 with America. It is, however, rare that this state 

 of affairs should survive his return more than a 

 few months. 



