Septembkr 10, 1915] 



SCIENCE 



329 



that the quantity of mathematical output on 

 the part of the Americans is, or has ever been, 

 such as to justify the statement that the con- 

 ception of making quantity the sole criterion 

 in regard to mathematical activity originated 

 with us. As regards quantity we never had 

 any mathematical writer who could be com- 

 pared with Euler, Cauchy, or Cayley. 



It is true that in recent years the quantity 

 of American mathematical literature has in- 

 creased rapidly, but the same is true in regard 

 to this literature in several other countries. 

 As evidence of the fact that the United States 

 is not inclined even at the present time, to go 

 to excess in regard to the quantity of its 

 mathematical literature we refer to the recent 

 publications under the general direction of the 

 International Commission on the Teaching of 

 Mathematics. At the Paris Conference held 

 in April, 1914, the estent of these publications 

 reported by various countries was as follows : 



Country No. of FageB 



Germany 3,822 



Austria 690 



Belgium 348 



Denmark 107 



iSpain 165 



United States 670 



France 674 



Holland 151 



Hungary 130 



British Isles 853 



Italy 253 



Japan 788 



Eoumania 16 



Russia 254 



Sweden 229 



Switzerland 812 



As questions relating to teaching offer 

 unusual opportunities for extensive publica- 

 tions the above table is very instructive as 

 regards tendencies towards quantity along 

 mathematical lines. It seems therefore un- 

 likely that Professor Borel had mathematics 

 in mind when he referred to our undue em- 

 phasis on quantity. It is much more likely 

 that he was impressed by the fact that our 

 conversation and our newspapers are so largely 

 confined to questions of quantity. In a com- 

 paratively new country the changes as regard 



quantity are so rapid as to attract wide atten- 

 tion, and these changes furnish the easiest 

 topics of conversation. Changes as regards 

 quality may be no less rapid but they furnish 

 less harmless subjects of conversation in view 

 of inherent difficulties and room for differences 

 of opinion. 



It is perhaps unfortunate that our conversa- 

 tion even in regard to intellectual matters is 

 so commonly directed by a desire to offend no 

 one instead of by a desire to call attention to 

 what is very important. The thoughtful for- 

 eigner who comes into our midst is thus nat- 

 urally impressed by the fact that we so com- 

 monly speak of harmless quantity instead of 

 the more important quality. Some years ago 

 while talking with a great French mathemati- 

 cian I was much impressed by the fact that, 

 in speaking about two of his eminent col- 

 leagues, he was very free in saying which of 

 the two he regarded as the more eminent. I 

 felt then that in America I would probably not 

 have found such voluntary reference to such a 

 delicate matter. 



The seriousness of this question becomes 

 apparent if it is observed that the tendency to 

 refrain from referring to quality in a public 

 way is reflected to some extent in the life of 

 the people. If in a university community, for 

 instance, it is regarded as undesirable to refer 

 to the quality of the work of the various mem- 

 bers of the faculty, and if the quantity of 

 salary is the sole index of relative standing, 

 there is apt to be little effort on the part of the 

 younger men to attain to a greater degree 

 of efficiency. Many questions of quality 

 appear shocking only in view of their 

 newness. After they have passed into the 

 stream of allowable conversation topics they 

 are not likely to offend anyone and they often 

 serve a useful purpose. In fact, the inefficiency 

 of a university professor often becomes a per- 

 fectly harmless topic. The danger lies in the 

 early stages towards such publicity as regards 

 the true conditions, and it is here where there 

 is usually the greatest field of usefulness. 



The greatness of a nation in the intellectual 

 and moral life is largely influenced by its em- 

 phasis on quality. Professor Borel urges that 



