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458 solution of this question. It is interesting to note that a young American mathematician, Professor G. D. Birkhoff, of Harvard University, had been thinking along similar lines and soon succeeded in finding a general solution. An article containing this solution was published in the Transactions of the American Mathematical Society, 1913, and a French translation of this article appeared recently in the Bulletin of the French Mathematical Society.

A number of important unsolved mathematical questions are constantly kept before the mathematical public by means of prizes offered by various foreign academies for definite contributions. The prominence of the Paris Academy of Sciences along this line is well known, and it would be difficult to determine the extent of the good influence exerted by these prizes. Moreover, special prizes are not infrequently instituted. The king of Sweden has recently authorized such a prize to be awarded, for important developments in the theory of analytic functions, during the meeting of the sixth international mathematical congress, which is to be held at Stockholm in 1916.

The monetary value of these prizes varies very much, but it generally does not exceed a thousand dollars. For instance, the prize offered by King Gustav V, of Sweden, to which we have just referred, consists of a gold medal and three thousand crowns (about eight hundred dollars) in money. The main value attached to these prizes is the recognition of the importance of the work of the authors honored in this manner, and this is especially valued by the younger investigators.

While prizes have greatly stimulated research activity in mathematics they have not furnished the main stimulus. The opportunities offered by the various journals to make useful development and interesting discoveries promptly known have doubtless furnished a stronger and more permanent stimulus, especially in those cases where the standing of the editors of the journals inspired great confidence. In America we have two journals which have rendered, and are now rendering, preeminent service along this line; viz., the American Journal of Mathematics, founded in 1878 with J. J. Sylvester as editor-in-chief, and the Transactions of the American Mathematical Society, founded in 1900 with E. H. Moore as editor-in-chief.

A current mathematical undertaking whose bigness would seem to entitle it to general interest is the publication of a large encyclopedia devoted to pure and applied mathematics. This work is being published, in parts, in the German and French languages. The first part of the German edition appeared in July, 1898. Since this time a large number of other parts have appeared at irregular intervals, aggregating at present about ten thousand large pages. Several additional parts are now in press, and it seems too early to predict when the entire work will be completed or how large it will become. The published parts would now