Page:Popular Science Monthly Volume 85.djvu/465

Rh, thought is developed along these mathematical roads, and the traveler finds continually new difficulties whose solution depends largely upon those encountered earlier. In constructing these roads mathematics is not seeking an intellectual monopoly in order to collect toll from the rest of the intellectual world in succeeding ages. In fact, in most of the newer regions the travelers are too few to encourage such thoughts even if they were not intrinsically repugnant.

There is, however, a considerable number of mathematicians who are interested in constructing unusually attractive toll roads, especially in those regions where travelers are most abundant. Whether the prospects of tolls derived from small royalties constitute the best means to secure improvements in our elementary text-books and whether this system is apt to continue to be efficient are questions which present many difficulties. There appears to be an enormous waste along this line at present resulting from unfruitful duplication.

The financial questions involved in mathematical publications have doubtless much in common with those relating to the publication in other subjects. The journals depend largely upon the universities and the mathematical societies for financial assistance. Lately the American Mathematical Monthly, a journal of collegiate grade, has received financial assistance from more than a dozen colleges and universities, and it has thus been enabled to make many improvements. The Annals of Mathematics, which is a journal of a somewhat more advanced grade, is being published since 1911 under the auspices of Princeton University.

The large mathematical encyclopedias, mentioned above, are being published under the auspices of the Academies of Göttingen, Leipzig, Munich and Vienna, while various governments have been asked to assume the expense of the publication of at least some of the reports prepared under the general direction of the International Commission on the Teaching of Mathematics. The Japanese reports are published both in the Japanese and in the English languages; and all these reports, aggregating already more than ten thousand pages, are for sale by Georg & Co., Geneva, Switzerland.

While mathematical societies generally support publication of advanced grade, they usually have other functions. In many instances membership implies attainments of comparatively high order and hence is attractive in view of the honor and exclusive privileges which it involves. Recently an international mathematical society has been organized with the sole purpose of supporting the publication of the complete works of the most prolific mathematical writer, Leonhard Euler, who died in 1783. Each member of this society is expected to pay at least ten francs annually until this publication is completed, which is expected to require about fifteen years.

Several years ago it was estimated that the complete works of Euler