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 equations." 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 mathematical ignorance of the average educated person has always been complete and shameless," 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 statement: "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 encyclopedias which are now in the process of publication. All large mathematical histories have appeared in foreign languages.
- New International Encyclopedia (1904), under "Substitutions."
- "Easy Mathematics," 1906, preface.