164 MATHEMATICS 



France in Mathematics. He was in a special sense their 

 master, equally great as teacher and scholar, and, in the 

 wide field he covered, typical of the modern school. 

 Among the notable contributors of this period was CHASLES. 



The present era in French mathematics may be said 

 to date from the early work of DARBOUX and JORDAN, in 

 the late sixties and early seventies. In rapid succession 

 appear the names of PICARD, POINCARE, APPELL, PAIN- 

 LEVE, GOURSAT, HADAMARD, and BOREL. Nor have the 

 achievements of the still younger group given ground to 

 believe that successors will be wanting. The brilliance 

 of the modern school has been enhanced by the broadness 

 of its leaders' achievements; the contributions of PICARD, 

 POINCARE, and HADAMARD, for example, have been re- 

 markable in geometry, algebra, and applied mathematics, 

 as well as in analysis. The latter field has, however, 

 been perhaps the most cultivated. 



No account of recent French mathematics can be com- 

 plete which fails to yield its tribute to the genius of 

 POINCARE. At his death, in 1912, it was the universal 

 verdict that he must be considered the greatest mathe- 

 matician of his age. 



Mathematicians of Today and their Work. It has 

 undoubtedly been true for many years that the group of 

 mathematicians resident in Paris was the most distin- 

 guished to be found at any one place in the world, and 

 there is no reason to believe that this situation will soon 

 be altered. The centralization of French scientific 

 activity presents distinct advantages to the mathematical 

 student from abroad, especially to the man of more mature 

 type. The older and more eminent mathematicians are 

 grouped in Paris. However, many of the provincial 

 universities have on their faculties one or more men, 

 usually of the younger scholars, who have such special 



