president's address — SECTION A. 7 



One of the last — if not the very last — of the public utterances of 

 Darwin was a tribute to the unique position occupied in the scientific 

 world by Poincare, the other great man whose loss to-day we mourn. 

 In August of last year Darwin was President of the International 

 Congress of Mathematicians at Cambridge. At its opening meeting his 

 earliest words were devoted to the expression of their heartfelt sorrow 

 at the sudden death of Poincare a lew weeks before in Paris. He 

 described him as the man who alone among mathematicians could 

 have occupied the position of President without misgivings as to his 

 fitness. It brought vividly home to him how great a man Poincare 

 was when he reflected that to one incompetent of appreciating fully 

 one half of his work, he yet appeared a star of the first magnitude. 



By universal consent Poincare was regarded as the greatest 

 mathematician of his time. Philosophers, mathematicians, and 

 astronomers looked to him as the leading authority in each of their 

 domains. Gauss, the famous geometer, the master of analysis, the 

 great astronomer, had won for himself the title Princeps Mathemati- 

 corum. Since his day the title had been vacant. With the coming of 

 Poincare his successor appeared. Now, when Poincare seemed in the 

 very fulness of his powers, his throne is vacant, and it is impossible to 

 measure the loss the world has sufiered. 



There are before me doubtless some who imagine that at the end 

 of their three years' course in Mathematics our students should have 

 been brought at any rate within sight of the confines of the subject. 

 A glance at Poincare's works would be sufficient to remove such a 

 thought from their minds. 



In Mathematics, as in every other science, one height is reached 

 only that from it we may press on to regions until then imknown. And 

 the man is best equipped for this exploration who has travelled widely 

 in the regions already discovered. We meet Poincare first of all as a 

 Pure Mathematician. To the whole modern Theory of Functions he 

 made contributions of the highest importance. An instance of the 

 way in which, even in his younger days, he was able to draw upon one 

 branch of Mathematics to help him in another is to be found in the 

 quaint description he has given of the manner in which he was led to 

 one of his earfiest discoveries. At that time he was about 27 or 28 years 

 of age, had graduated from the School of Mines, and had just received 

 his Doctorate in Mathematics from the University of Paris. For we 

 must not forget that Poincare was one of those mathematicians who had 

 a complete training in physical science, as well as the course in Pure 

 Mathematics for which the French School is famous. 



He tells us that for about a fortnight he had been trying to 

 demonstrate the existence of functions analogous to those which he 

 afterwards discovered and called Fuchsian Functions. Every day he 

 %vould sit at his table for an hour or so ; attempt a number of 



