AMERICAN MATHEMATICS 459 



AMERICAN MATHEMATICS 



By Professor G. A. MILLER 



UNIVERSITY OF ILLINOIS 



ABOUT a dozen years ago a well-known French mathematician 

 wrote as follows in reference to our mathematical situation: 1 

 " Mathematics in all its forms and in all its parts is taught in numerous 

 [American] universities, treated in a multitude of publications, and 

 cultivated by scholars who are in no respect inferior to their fellow 

 mathematicians of Europe. It is no longer an object of import from 

 the old world but it has become an essential article of national produc- 

 tion, and this production increases each day both in importance and in 

 quantity." 



Taken by itself this assertion looks good and it is doubtless more 

 nearly true to-day than it was at the time of publication. If we turn 

 our eyes away from this statement and rest them upon the mathematical 

 book shelves of a good library, we can not fail to notice that our accom- 

 plishments do not seem to be in accord with the complimentary state- 

 ment noted above. This disaccord will become still more evident if we 

 look through the pages of some of the standard works of reference, such 

 as the great mathematical encyclopedias which are now in the course of 

 publication. 



If a student of the history of mathematics would make a list of the 

 leading mathematicians of the world during the last two or three cen- 

 turies, arranging the names in order of eminence, he would have a fairly 

 long list before reaching the name of an American. Such names as 

 those of Euler, Cauchy, Gauss, Lagrange, Galois, Abel and Cayley have 

 no equals in the history of American mathematics; and, among living 

 mathematicians, probably all students would agree that there are no 

 American names which should be placed on a mathematical equality 

 with those of Poincare, Klein, Hilbert, Frobenius, Jordan, Picard and 

 Darboux. Both of these lists of names could be considerably extended 

 without any danger of being unfair to the mathematicians of this coun- 

 try, but they suffice to establish the fact that our mathematical situa- 

 tion is not yet satisfactory, notwithstanding our remarkable progress 

 during recent decades. 



This unsatisfactory situation is reflected in many of our standard 

 books of reference. For instance, under such an important word as 

 " matrix" one finds in Webster's New International Dictionary (1910) 



1 Laisant, "La Mathematique, Philosophie-enseignement, " 1898, p. 143. 



