MODERN MATHEMATICAL RESEARCH MILLER. 195 



work v/hich is being clone by the Royal Society of London — not only 

 for mathematics, but also for a large number of other sciences — in pro- 

 viding bibliographical aids on a large scale. If the increase in knowl- 

 edge will always be attended by a corresponding increase in means to 

 learn readily what is known, even the young investigator of the future 

 will have no reason to regret the extent of the developments. On the 

 contrary, these should make his task easier, since they furnish such a 

 great richness of analogies and of tried methods of attack. 



The last two or three decades have witnessed a great extension of 

 mathematical research activity. As a result of this we have a large 

 number of new mathematical societies. A few of the most recent 

 ones are as follows: Calcutta Mathematical Society (1908), Man- 

 chester Mathematical Society (1908), vScandinavian Congress of 

 Mathematicians (1909), Swiss Mathematical Society (1910), Spanish 

 Mathematical Society (1911), and the Russian Congress of Mathe- 

 maticians (1912). In Japan a new mathematical periodical, called 

 Tohoku Mathematical Journal, was started in 1911, and a few years 

 earUer the Journal of the Indian Mathematical Society was started 

 at Madras, India. The Calcutta Mathematical Society and the 

 Spanish Mathematical Society have also started new periodicals 

 during the last two or three 3^ears. 



While there has been a very rapid spread of mathematical activity 

 during recent years, it must be admitted that the greater part of the 

 work which is being done in the new centers is quite elementary from 

 the standpoint of research. The city of Paris continues to hold its 

 ])reeminent mathematical position among the cities of the world, 

 and Gei-many, France, and Italy continue to lead all other countries 

 in regard to the quahty and the quantity of research in pure mathe- 

 matics. 



Although America is not yet doing her share of mathematical 

 research of a high order, we have undoubtedly reached a position of 

 respectabiUty along this line, and it should be easier to make further 

 progress. ]\Ioreover, our material facilities are increasing relatively 

 more rapidh^ than those of the countries which are ahead of us, and 

 hence many of our yoimger men start under very favorable condi- 

 tions. Unfortunately, there is not yet among us a sufTiciently high 

 appreciation of scholarly attainments and scientific distinction. The 

 honest and outspoken investigator is not always encouraged as he 

 ought to be and the best positions do not always seek the b(^st man. 

 I coupled "outspoken" with "investigator" advisedly, since research 

 of high order implies Ubei'ty and scorns shams, especially shams relating 

 to scholarship. ICven along these lines there seems to be encourag- 

 ing progress, and Ihis jirogrcss may reasonably be expected to increase 

 with the ])asshig of those who belong to the ])ast in si)int and attain- 

 ments. What appears to be a very serious element in our situation 

 is the fact that the American imiversity professor does not yet seek 



