462 TEE POPULAR SCIENCE MONTHLY 



As a result of this lack of intermediate mathematical literature 

 comparatively few of our people know what constitutes a mathematician 

 of high order. The time has been when even the educated public 

 seemed to believe that the author of a successful series of elementary 

 text-books had necessarily gained a place among the great mathemati- 

 cians of the world. As several of our most popular recent series of 

 text-books were edited by men of remarkably low mathematical attain- 

 ments, this view is no longer so generally held, but it is questionable 

 whether it has been replaced by a more correct one on the part of the 

 majority of those who feel entitled to express an opinion on the work of 

 mathematicians. 



In looking over the work of the fourteen great mathematicians men- 

 tioned above one finds that all of them published mathematical articles 

 and that a majority of them also published treatises. Two of them, 

 Abel and Galois, died at an early age, before they had time to develop 

 sufficiently the fields in which they were interested to write extensive 

 treatises. This is especially true of Galois, who published only five 

 papers during his short lifetime of only twenty years, but several of his 

 other papers appeared later. 



The extent of the publications of the mathematicians mentioned 

 above varies from the comparatively few brief articles by Galois to the 

 voluminous publications by Euler, which are just now appearing in a 

 collected form and are expected to fill forty large volumes. Judging 

 from the great mathematicians of the recent past, it would appear that 

 publication of original articles is one essential of greatness, but great- 

 ness is not measured so much by the number and the extent of such 

 publications as by their merits. It should, however, be observed that 

 nearly all of the great mathematicians of the recent past have published 

 a large number of research papers. In the case of Cayley, who is the 

 only Englishman in the given lists, the number of these papers is about 

 one thousand. 



America has never had a mathematician who published as exten- 

 sively as some of the European mathematicians, and the average ex- 

 tent of our publications is much below the average of the leading 

 mathematical countries of Europe, if we exclude the elementary text- 

 books. It is doubtless true that the most important consideration at 

 present is the improvement of the quality of our publications, but we 

 are also in need of more mathematical journals to insure more rapid 

 publication of good research material. If the crowded condition of our 

 research journals would induce a larger number to assist in bringing out 

 more good intermediate mathematical literature, it would doubtless be 

 of great importance for the future advancement of the science. 



One of the leading agencies in bringing about rapid mathematical 

 advances during the last few decades is the American Mathematical 



