458 TEE POPULAR SCIENCE MONTHLY 



eral solution of this question. It is interesting to note that a young 

 American mathematician, Professor G. D. Birkhoff, of Harvard Univer- 

 sity, 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 con- 

 stantly 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 dis- 

 coveries 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 Trans- 

 actions 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 pres- 

 ent 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 



