viii OBITUARY NOTICES OF MEMBERS DECEASED. 



sufficient to rank him ahead of most of his contemporaries. One 

 thinks first perhaps of his two papers on the uniformization of a 

 general analytic function which appeared in 1883 and 1908 respec- 

 tively. Then there are his papers on transcendental entire functions 

 and on analytic functions which have lacunary spaces. He made 

 several contributions to the theory of Abelian functions, the reduc- 

 tion of Abelian integrals, the theory of the zeros of theta functions. 

 His paper on linear equations of finite differences has stimulated a 

 great activity of research in that field. In Liouville's Journal for 

 1890 he investigated sets of functions satisfying what he called a 

 theorem of multiplication, including particularly a new class of func- 

 tions which he named after Cremona. He also deserves credit for 

 establishing the convergence of Hill's infinite determinant and wrote 

 several papers on integral equations and their applications. Also 

 several papers on continuous groups, on hypercomplex numbers, on 

 number theory, and on the relation of automorphic functions to 

 number theory.^ 



The mathematical style of Poincare was intensely modern. There 

 are few purely formal theorems to his credit. Few of his results 

 depend on long or difficult computations. He said of himself with 

 a furtive touch of humor — the remark came in a paper relating to 

 his and Darwin's work on the pear-shaped figures — that he was poor 

 at arithmetic. He was good, on the other hand, at divining- a gen- 

 eral principle after seeing the least possible number of special cases. 

 He was tremendously powerful at the essentially modern game of 

 finding out all about a function irrespective of whether it could be 

 adequately described by formulas of the classic type. In any prob- 

 lem he felt instinctively for the fundamental group and for the in- 

 variants thereof. He had an almost visual grasp of the properties 

 of a figure of any number of dimensions which remain invariant 

 imder a continuous deformation, and this either in case of the small 

 ■deformations that are considered in problems of stability or in the 

 larger ones that constitute the subject matter of analysis situs. All 

 this was combined with a sound judgment which always directed his 



*A satisfactory bibliography of Poincare's publications is to be found in 

 ""Savants du Jour, Henri Poincare," by E. Lebon (Paris, 1912). 



