272 THE POPULAR SCIENCE MONTHLY 



was to classify the results established, to study their connections, with 

 no care for the demonstrations, sure of finding others, if you happened 

 to forget the ones which they had employed; at the time of your 

 entrance examination, did you not find a new solution for a problem 

 which had been set you? When you worked, you did not remain in 

 your room, but gave your brain a promenade through the corridors, 

 and in place of a pen, a pencil or a piece of chalk, your hand was busy 

 with a bunch of keys — your opener of ideas. 



Your superiority in mathematics was so decided that, in spite of 

 your inaptitude for anything practical — manipulations, linear design, 

 imitative design — you were, at the closing examination, placed second, 

 and admitted to the School of Mines. There you found life pleasant 

 for more than one reason. In the first place, in the Latin Quarter, 

 you lodged with one of your cousins, who was taking a literary and law 

 course. . . . With him, in the practise of peripatetism — which was, 

 perhaps, less a philosophical school than a physical peculiarity of philos- 

 ophers and mathematicians — you followed those studious rounds in the 

 course of which you discussed philosophic themes, already indissolubly 

 associated in your mind, as in those of the ancients, with mathematical 

 theories. 



In 1880, the Academy of Sciences had set as the subject of the 

 mathematical great prize, the theory of differential equations. When 

 the illustrious M. Hermite presented his report, he mentioned a dis- 

 cussion bearing the motto: Non inultus premor, whose anonymous 

 author he invited to persevere in a work which promised to produce 

 results. The motto was that of Nancy ; you were the author ; but your 

 paper was only a first sketch; you presented at that time only the 

 results which you were soon to obtain and which, in the month of 

 February, 1881, burst forth — it is the only exact phrase, says one of 

 your admirers — in the report of the Academy of Sciences. From week 

 to week, with the notes which you sent out regularly, your discovery 

 increased in precision and amplitude for a period of nearly two years. 

 Your contribution was the "the crowning of the work of Cauchy and 

 Eiemann, the representation of the coordinates of any algebraic curve 

 in uniform functions, the integration of linear differential equations 

 with algebraic coefficients — it was a new and immense perspective 

 opened to view." 



This discovery was a great victory for French science. For some 

 years the German geometers had been roving about the house without 

 finding the door. You located it and opened it. 



From there I need not follow you in your career: Professor in the 

 University of Paris and the Ecole Polytechnique, your lessons have had 

 an unequaled vogue; and if, among your auditors, many were not able 

 to follow you, all agreed in proclaiming your astonishing superiority; 

 at thirty-two years you were elected 'a member of the Academy of 



