Jacques Hadamard, 1865-1963

Abstract

Jacques Hadamard died on 17 October 1963 at the age of 98. He published his first mathematical paper of importance in 1888, and continued working until he was over 90 covering an immense range of mathematical subjects including educational, philosophical and psychological aspects of mathematics. To classical analysts his name has been well known as the author of the Hadamard gap theorem, the Hadamard three circle theorem , the Hadamard factorization theorem for integral functions and other results on Taylor series published before 1900, but perhaps it was his proof of the prime number theorem in 1896 more than anything else which made Hardy describe him in 1944 as the ‘living legend’ in mathematics. To some pure mathematicians he may be better known by his theorem on the modulus of a determinant which plays such an essential part in the Fredholm theory of integral equations, or because he invented the name for functional analysis. His work on the theory of propagation of waves and partial differential equations was no less significant, but it is less easy to pinpoint particular results. It is at the base of the modern theory of both subjects; it includes much work on the Cauchy problem and on the technique of the finite parts of integrals which, although superseded by the theory of distributions, proved to be very useful. He was no physicist, but he helped to lay the foundations of the modern theory of shock waves. No one person could do justice to such an enormous range of mathematical activity which was matched by wide interests outside mathematics, and what I have to say owes much to the assistance of others. In particular Mile Jacqueline Hadamard has supplied me with much information and copies of articles and speeches about her father, but, owing to the fact that all their belongings were stolen by the Germans during the war, and also, because as she admitted, ‘he had so little order and method, keeping everything about others and so little about himself’, the information, and in particular the list of published work, is probably incomplete, and the latter is certainly difficult to check. There are over 300 items, many of them published long ago in periodicals not easily traced from the brief descriptions given in the list in the Selecta [284].* I have drawn largely from speeches made at his Scientific Jubilee [284a] in 1936, from articles by Lévy, Mandelbrojt, Fréchet, Julia and Kahane and from Hadamard’s own accounts of events and influences extracted from various articles, books and speeches. I am also particularly grateful to Professor Fréchet, Professor Leray, Professor Kahane, Professor Temple, Professor G. N. Ward, Mr A. E. Ingham, Professor Truesdell, Dr F. G. Friedlander, Dr L. S. Bosanquet and Sir Edward Collingwood for their help. * Numbers in square brackets refer to the numbered items in the bibliography described at the end of the memoir, pp. 96 to 99.