From a topological theory of semigroup to a geometric one.
This paper examines developments in the study of boundary-value problems between about 1860 and 1890, in the context of the general evolution of this theory from the physical models in which the subject has its roots to a free-standing part of pure mathematics. The physically-motivated work of Carl Neumann and his method of the arithmetic mean appear as an initial phase in this development, one which employs physical models as an integral part of its reasoning and which concentrates on geometrical...
Starting from the famous Königsberg bridge problem which Euler described in 1736, we intend to show that some results obtained 180 years later by König are very close to Euler's discoveries.
This is the second in a series of two papers on numeration schemes. Whereas the first paper emphasized grouping as exemplified in the partition of a number so as to obtain its base two numeral, the present paper takes at its point of departure the method of repeated divisions, as in the calculation of the base two numeral for a number by dividing it by two, then dividing the quotient by two, etc., and collecting the remainders. This method is a sort of classification scheme - odd or even.
Cet article examine comment la notion d’espace vectoriel de fonctions s’est peu à peu imposée dans l’analyse entre 1880 et 1930 environ. Malgré certaines approches formelles précoces, les questions linéaires en dimension infinie sont longtemps restées marquées par l’analogie avec la dimension finie, que l’on traitait alors à l’aide des déterminants. Nous regardons comment l’étude de l’équation de Fredholm d’une part, en particulier le travail de Hilbert, et l’émergence de notions topologiques d’autre...