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 philosophers 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 discussion 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 Riemann, 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 École 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
