JULES HENRI POINCARE. 



(Read December 6, icjij.) 



In a much quoted sentence, Klein has said " We shall have a pic- 

 ture of the development of mathematics if we imagine a chain of 

 lofty mountains as representative of the men of the eighteenth cen- 

 tury, terminating in a mighty outlying summit, — Gauss, and then a 

 broader, hilly country of lower elevation ; but teeming with new ele- 

 ments of life." This was written in 1893 and would perhaps still 

 be received as the truth by most observers. During the ensuing 

 period it has, however, become more and more evident that two of 

 the contemporary hills rise quite above the others, and it may be that 

 when they are seen in perspective they will compare favorably with 

 the more distant mountains. 



Hilbert and Poincare are associated and contrasted in the minds 

 of all students of mathematics both by the brilliance of their achieve- 

 ments and the difference of their methods. To enter into a com- 

 parative study of these two great men would not be an appropriate 

 exercise for this occasion, but to have suggested it may help to indi- 

 cate the relation of Poincare to the time in which he lived. 



Aside from his intellectual triumphs, which one could adequately 

 comprehend only by reading a series of his papers, the life of Poin- 

 care presents little of interest. He was born at Nancy on the 29th 

 of April, 1854. His unusual gifts were recognized early, so that he 

 had an excellent education. He received the degrees of Bachelor of 

 Letters and of Science in 1871 and that of Mining Engineer in 1879. 

 He was attached in one capacity or another to the Department of 

 Mines of the French government for the rest of his life, but not in 

 such a way as to interfere with his scientific work. 



In the year 1879 he also received his doctorate of Science from 

 the L^niversity of Paris. He was immediately made a member of 

 the faculty of science at Caen. From there he was called to the 

 University of Paris in 1881. In 1886 he was appointed professor 



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