[aRcHIBALD] MATHEMATICAL INSTRUCTION IN FRANCE 123 
Such are the standards set for those, who have prepared them- 
selves as lycée professors, who direct the boy’s education from the 
time he is ten years old. How woefully low are our standards in com- 
parison! Remark too, that after a boy is 6 years old he is taught 
by men only. 
We are also struck with the breadth of the future mathematician’s 
training. Although it is true that after the age of 16, the humanities 
are set aside, yet physics, descriptive geometry, pure mathematics, 
applied mathematics, all continue to occupy positions of importance. 
I have indicated how, by peculiar method of instruction, all these 
subjects are welded into a homogeneous whole, how that although 
knowledge of wide range of fact is fundamental, it is the thorough 
grasp of broad principles and the powers of ready application of those 
principles to the most diverse kind of problems, that is made essential. 
German influence has given us a great respect for fact, but the French, 
if opportunity were given, would soon convince us that a fact, as a fact, 
had little of interest, except in so far as it might be contributary to 
the upbuilding of some system. To the Frenchman learning is not an 
accomplishment, but ‘an honourable and arduous profession with all 
its trials, all its heart-burning competitions, all its pitiless disdain of 
weakness, all its stimulating rewards.” This partly explains the se- 
verity of the examinations. Every boy of remarkable intellect, be he 
rich or poor, has the chance to have his talents developed to the ut- 
most. From the time he is 11 or 12 years old till he is ready to step 
into a position in a university, bursaries constantly reward his accom- 
plishment. If in time he become professor in a provincial university, 
his effort is in no whit relaxed; he looks forward to being promoted 
to Paris. With this advancement accomplished, his intellectual ac- 
tivity does not cease by any means, for he now hopes some day to 
be numbered among the few members of the Académie des Sciences 
of the Institut. Great as are the rewards and recognition of merit 
here, there is still greater for him who, as Poincaré, is pre-eminent, 
namely, to be numbered among the “immortals” of the Académie 
Française of the Institut. Men of such calibre and brilliance and un- 
remitting intensity of application and purpose, are the professors at 
the Collége de France and Université de Paris. 
Nothing in French universities takes the place of undergraduate 
life in England and America; nor would we willingly attempt to adopt 
their system, though it would certainly silence the frequent criticism 
of our ordinary B.A. course, namely, that it is, to say the least, a poor 
training for the future man of business; the student has few obliga- 
tions to meet, no real obstacles to overcome; if the professors make 
the courses difficult, he either rises in protest or seeks a college with 
