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[arcæiBALD] MATHEMATICAL INSTRUCTION IN FRANCE 117 
is about as high as for the doctorat de l’état. It is in the matter of 
further requirement that the doctorat d’état is more difficult. For 
this degree there is no possible way of avoiding the various examin- 
ations which lead up to the licence és science with mention of the 
certificats: 1st, calcul différentiel et intégral; 2nd, mécanique ration- 
nelle, and 3rd, at the choice of the candidate. For the doctorat de 
l'Université! only two certificats are required, and, in the case of 
foreigners, very great latitude is permitted the faculty in accepting 
equivalents for these certificats, in view of work done elsewhere. 
In both cases only one year of residence is required. We can, then, 
now answer the second question, proposed above, in the affirmative 
for the doctorat de l’Université, and in the negative for the doctorat 
d’état. 
The analytical table given in Appendix C clears up misconception 
as to the age of the French mathematical doctor. During the past 25 
years, the average age has been 30, but a large number “sustained” 
their théses between the ages of 23 and 25. The youngest doctor was 
Joseph Louis Francois Bertrand, aged 17, created in 1839; the oldest, 
in 1882, aged 55. 
Only a small proportion of the agrégés ever become doctors,’ 
and in but one case (1894) has a doctor become an agrégé. Which title 
calls for the greater ability in the getting?* The two things are so 
entirely different, it is perhaps difficult to understand why some say 
the doctorate ranks the higher. The musician with great technical 
talent only, may be allowed to have equal ability with the performer 
less gifted in this direction but endowed with strong temperament— 
power of perception and interpretation which draws aside the veil 
for the ordinary observer and discloses formerly hidden heights, beyond. 
Yet it is the latter who particularly appeals to us. So while the tech- 
nical skill of the agrégé is admired, and the state gives him certain rights 
denied the doctor, it is only the latter who, on showing power of dis- 
closing the truths waiting for discovery from the foundations of the 
worlds, has the opportunity to direct the nation’s youth in the great 
universities of the country. So much the more sought after the man 
who combines in himself to a high degree both talents, the gift of 
brilliant exposition and the genius for discovery. 
The general procedure toward the doctorate is the same for 

1 According to a decree of 1906 the insignia of the docteurs de l’université de 
Paris is, “ Epitoge à trois rangs d’hermine, avec les couleurs de Paris (bleu et rouge) 
dans le sens longitudinal.” 
2 Cf. Appendix A. 
3 The agrégé in Law and Medicine stands much higher than the doctor in these 
Departments. 
