Jdne 17, 1921] 



SCIENCE 



547 



writing should be laid upon the opening para- 

 graph. I suggest that without exception the 

 introduction should be framed about the 

 thought " this is an interesting and worth- 

 while contribution" (if the author has not 

 this conviction, he ought not to ask it of the 

 editor) ; that it ought therefore to give the 

 historical setting of the problem in hand, an 

 indication of its relationship with other prob- 

 lems of established importance or of recog- 

 nized interest, either in mathematics or in 

 allied sciences, with a clear indication of the 

 novelty claimed in results or methods or 

 presentation. If the author will then outline 

 his general course of reasoning, he will fur- 

 tlier enhance the readability of his paper. 

 Similar remarks apply to the presentation of 

 papers at meetings of scientific societies. A 

 paper should be made interesting, or be read 

 by title. As long as the author conceives it 

 to be an act of merit merely to go through the 

 form of presenting a paper, so long will he 

 deserve to have his audience melt away to 

 talk of really interesting things in the corri- 

 dors. It is, to be sure, a difficult task to make 

 a highly technical subject of general interest, 

 but it can be done by a placing of emphasis 

 more on setting and less on detail, and the 

 efFort is a scientific duty. 



I have alluded to the question of values. 

 There is another side to this question, or per- 

 haps rather another aspect of values that must 

 not be overlooked. I have heard the question 

 raised as to where or when our American La- 

 Granges are to appear. There is little doubt 

 but that young men of a high degree of genius 

 exist in this country in every generation. 

 That more of them do not find their way into 

 mathematics, or, having found their way, 

 do not continue on and develop there, is, to a 

 considerable extent, a matter of environment. 

 By cultivating a backgrovmd of productive 

 scholarship, by cultivating an appreciation of 

 productive scholarship, something can be done 

 toward producing a favorable environment. 

 TJsusally men of genius are as sensitive to ap- 

 preciation, as responsive to encouragement, 

 as any one else. The geniuses must have their 

 audience of appreciative scientists, the less 



gifted producers must have their audience of 

 interested readers, and the science as a whole 

 must have a hold on popular respect. 



Now nothing enhances a man's mathe- 

 matical interests like a share in the develop- 

 ment of the science, even though the share 

 have but slight intrinsic importance. It 

 seems to me therefore that it is desirable to 

 have means of publication of papers of minor 

 importance — it being imderstood that in re- 

 spect to content or method some novelty and 

 merit is present — both because the encourage- 

 ment thus given may at any time be the oc- 

 casion of stimulating eiiort destined to be- 

 come of high value, and because the interest 

 engendered is likely, at the least, to become 

 a support to the more effective producers. 



Just as an enormous impetus to mathe- 

 matical work in this country was nearly co- 

 incident with the foundation of the New York 

 Mathematical Society, so also I think we may 

 reasonably look for a distinct impetus from 

 the founding of the Mathematical Association 

 of America, whose successful launching has 

 been one of the important scientific events of 

 the decade, and which has already brought to 

 light a lively group of mathematical interests 

 beyond the hope even of the founders. 



Various ways of external encouragement of 

 mathematical science in America have recently 

 been discussed. They include the items I 

 have mentioned, the encouragement of publi- 

 cation both of books and periodicals, they in- 

 clude prizes for important contributions, and 

 they include recommendations for diminish- 

 ing the distractions which hamper the scien- 

 tist in the way of excessive instruction and 

 administration. While I do not wish to sug- 

 gest that more effective means exist, nor to 

 imply that such steps ought not to be sec- 

 onded most heartily, I do wish to point out 

 that each individual can throw his added in- 

 fluence into the scale and help materially and 

 immediately, first by efforts to produce, in 

 the faith that such efforts will certainly re- 

 sult in his being more vitally a scientist and 

 a more enthusiastic teacher of his subject; 

 second, by cultivating a discriminating sense 

 of value, and endeavoring to throw his pro- 



