*RECENT MATHEMATICAL ACTIVITIES*

457

RECENT MATHEMATICAL ACTIVITIES |

By Professor 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 unsolved 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 special ingenuity or through the gradual development of the necessary elements, 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 mathematical 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 Émile Picard, that the memoir was epoch making for analysis and for mathematical astronomy. In accord with the recommendation of this committee, the Paris Academy awarded to Sundman the Pontécoulant prize, doubling its usual value. The report of the committee directed attention to the fact that Sundman achieved his results 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 Poincaré, 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. Poincaré, written shortly before his death, in which he called attention to the fact that he had not succeeded in finding a gen-