RECENT MATHEMATICAL ACTIVITIES 457 



KECENT MATHEMATICAL ACTIVITIES 



By Professoe G. A. MILLER 



UNIVERSITY OF ILLINOIS 



MATHEMATICAL research generally thrives best in seclusion. 

 The results are often embodied in a language which but few 

 understand, and are then stored with a quietude secured and maintained 

 by their own attributes. Now and then there are instances when un- 

 solved mathematical questions get involved with enough external matter 

 to attract general attention. This external matter often consists of an 

 array of names of noted mathematicians who have been unsuccessful in 

 their efforts to solve these questions. 



When the solutions of such questions become possible, through spe- 

 cial ingenuity or through the gradual development of the necessary ele- 

 ments, there is usually a. stir in which mathematicians join the more 

 heartily on account of its novelty. This fact may be illustrated by the 

 famous memoir on the problem of three bodies by a Finnish mathe- 

 matical astronomer named Karl F. Sundman, which the president of the 

 Paris Academy of Sciences mentioned during the annual public session 

 held on December 13, 1913. 



This academy had previously appointed a committee to examine the 

 work of Sundman, and the committee reported, through the noted 

 French mathematician Emile Picard, that the memoir was epoch mak- 

 ing for analysis and for mathematical astronomy. In accord with the 

 recommendation of this committee, the Paris Academy awarded to Sund- 

 man the Pontecoulant prize, doubling its usual value. The report of the 

 committee directed attention to the fact that Sundman achieved his re- 

 sults by means of classic mathematical methods. 



In the April, 1914, number of Popular Astronomy Professor F. E. 

 Moulton, of the University of Chicago, gave a very interesting popular 

 account of the problem of three bodies and of the actual contribution 

 made by Sundman towards its complete solution. From this account 

 it is easy to see that a long list of eminent names are connected with 

 this problem, including those of Newton, Euler, Lagrange and Poincare, 

 as well as that of one of the most illustrious American mathematical 

 astronomers — the late G. W. Hill. 



About two years ago a certain geometric question relating to the 

 problem of three bodies came suddenly into prominence through an 

 article by H. Poincare, written shortly before his death, in which he 

 called attention to the fact that he had not succeeded in finding a gen- 



