116 ROYAL SOCIETY OF CANADA 
Germany, where Berlin university turns out a very small fraction of the 
doctors in any one year—during 1906-08, less than 4 per cent. There 
is also one other great difference between French and German univer- 
sities, although the examinations for licenciés rather than those for 
doctors must be chosen to emphasize the point sufficiently. The diffi- 
culty of obtaining those degrees common to most French universities is 
much the same, and although Paris is the principal degree-conferring 
centre, it is well established that there have been years when it was 
more difficult to obtain the licence, in some departments, at certain 
universities of the provinces than at the Université de Paris. That 
the personality of the professor should play an important role in deter- 
mining the standard of excellence demanded is only natural; but as 
it is the ambition of every professor in the provinces to make his 
department important and to ultimately arrive at Paris, one can be 
very sure that no one university in France will ever sink to the level 
of at least two German universities, where, on account of lax demands 
in study and thesis, even train conductors call out “Twenty minutes 
wait to get your doctor.” 
But if such representative universities as Berlin, Gottingen, Munich 
be selected in Germany and compared with that at Paris, two questions 
suggest themselves: (1) Does the average doctor’s thesis (which in 
both countries is the essential performance on the part of the candidate 
for the degree) indicate a higher standard of excellence in one country 
than the other? (2) Admitting this to be the case, are the minimum 
requirements in this country as low as the general requirements in 
the other? By actual study of the theses, I am convinced that the 
answer to the first question is decidedly in favour of Paris. One could 
easily cite a number of French théses which were notable and extensive 
contributions to mathematical progress, but it is only necessary to 
refer the reader to the complete list of the théses, which is given in 
Appendix C. Before answering the second question, I shall explain 
more fully the nature of the French doctorate, the general conditions 
under which it is available for the Frenchman and the possible modi- 
fications of those conditions in the case of foreign candidates. 
There are two doctor’s degrees open to the mathematical student 
in France: the first, doctorat ès sciences mathématiques, conferred by 
the State (doctorat d’état), the second conferred by the universities 
—for the Sorbonne, doctorat de l’Université de Paris. Only one 
American, a woman, has won the former degree, which was created 
in 1810, and only one American has also obtained the latter, which 
was organized as recently as 1898. In both cases the thése is the prin- 
cipal requirement, and judging by the eight for which the doctorat 
-de l’Université de Paris has been granted, the standard in this respect 
