AMERICAN MATHEMATICS 461 



those who would be best qualified to render excellent service along this 

 line are unwilling to undertake it in view of the large amount of labor 

 which it involves. 



As an instance of a decided misstatement in one of the best of these 

 encyclopedias we may cite the following: " Sylow (1872) was the first 

 to treat the subject [substitutions] apart from its applications to equa- 

 tions." 2 Very little reading along the line of the development of the 

 theory of substitutions would reveal the absurdity of this statement. 

 Nearly all of Cauchy's fundamental work along the line of substitutions 

 was no more intimately connected with the theory of equations than the 

 articles by Sylow. Similar remarks apply to most of that part of 

 Jordan's work which antedates Sylow' s fundamental article, and also to 

 the work of a number of other authors. 



Judging from the following words of Sir Oliver Lodge ; " the mathe- 

 matical ignorance of the average educated person has always been com- 

 plete and shameless/' 3 one could not expect to find very much better 

 conditions in England. In fact, in consulting the large Murray English 

 Dictionary, published at Oxford, England, the writer found under the 

 first mathematical term which he consulted, viz., the word " group," 

 not only an incomplete definition, but also the following incorrect state- 

 ment : " The idea of group as applied to permutations or substitutions 

 is due to Galois." As a matter of fact, the idea of permutation groups 

 was clearly developed by Kufrini about thirty years before Galois, not to 

 mention the still earlier work by Lagrange and the early publications 

 of Cauchy and Abel. 



One of the most direct inferences from what precedes is the fact 

 that there is too much mathematical indifference. If more vigorous 

 protests against the inaccuracies in our standard books of reference 

 would be made, publishers and general editors would doubtless exercise 

 greater caution in the selection of their mathematical editors. This 

 mathematical indifference is perhaps still more disastrous when it exists 

 among university administrators. Judging from several of the recent 

 appointments in leading universities, it would appear that we are not 

 moving as rapidly towards high mathematical ideals as one might wish. 



The English-speaking pure mathematicians constitute more nearly 

 a terra incognita than the workers in any other large field of knowledge. 

 This is partly due to the nature of the subject and partly to the fact 

 that there are so few mathematical works of reference in the English 

 language. There never has been a good mathematical encyclopedia or 

 other work of general reference in this language, while the French and 

 Germans have had several such works in addition to the great encyclo- 

 pedias which are now in the process of publication. All large mathe- 

 matical histories have appeared in foreign languages. 



2 New International Encyclopedia (1904), under "Substitutions." 

 3 "Easy Mathematics," 1906, preface. 



