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90 ROYAL SOCIETY OF CANADA 
INTRODUCTORY. 
As the result of remarkable progress during the past fifteen years, 
a vigorous American School of Mathematics, of which the German 
School may well be considered the parent, has been developing. Many 
years must elapse before the offspring may exercise the authority and 
influence made felt by such masters as Gauss, Riemann, Steiner, Weier- 
strass and Klein. But meanwhile the process of evolution is proceeding 
in thorough fashion. In preparing for higher mathematical education, 
America has recognized the fundamental importance of the secondary; 
organization, discussion, and criticism of home methods as well as study 
of those of foreign countries, have been widespread in recent years. 
But here, again, the preponderance of discussion in book and periodical 
is of German methods. The series of reports of the Carnegie Founda- 
tion for the Advancement of Teaching is doing considerable to spread 
accurate informacion of a more general character. 
Yet in spite of the predominance of German influence in the dis- 
cussion, I have become convinced, after several months of observation, 
that just as much might be beneficially acquired by the study of mathe- 
matics and methods of mathematical training in France, as in any other 
country. Has not this country produced Chasles, Monge, Poncelet, 
Cauchy, LaPlace, Hermite? What city beside Paris has to-day such a 
large number of mathematicians of the first order? There are Poincaré, 
Darboux, Goursat, Picard, Painlevé, Appell, Jordan, Humbert, Borel, 
Tannery, to mention only a few. What other country gives such a 
course of mathematical training as is provided in the Classes de Mathé- 
matiques Spéciales of the French Lycées? Where else is the extraordi- 
narily high standard of the agrégation demanded of higher teachers in 
the secondary schools? 
Nevertheless when leaving Harvard some ten years ago with a view 
to further mathematical study in Europe, and although more or less 
familiar with such classic treatises as those of Darboux, Picard, Tannery, 
Appell and Goursat, I scarcely even considered France, as a possible place 
of location. The professors at Harvard who had studied abroad had 
been trained in Germany and were thoroughly imbued with German 
methods and ideals. The same was doubtless true of at least ninety- 
five per cent of the mathematical professors in the larger American 
colleges, and the same may be said to-day—Why this neglect of France? 
For one thing the American student usually looks forward to 
getting a doctor’s degree in one or two years, while the idea is certainly 
prevalent among us that if the French degree of doctor were at all 
available for the foreigner, he could only expect to get it at the age of 
forty-five or fifty, and after writing some monumental or epoch-making 
treatise. Such ignorance is without*doubt due in part to the excessive - 
