*THE 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 mathematicians of the world. As several of our most popular recent series of text-books were edited by men of remarkably low mathematical attainments, this view is no longer so generally held, but it is questionable whether it has been replaced by a more correct one on the part of the majority of those who feel entitled to express an opinion on the work of mathematicians.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 mentioned 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 greatness 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 extensively as some of the European mathematicians, and the average extent of our publications is much below the average of the leading mathematical countries of Europe, if we exclude the elementary textbooks. 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