A Little History

Abstract

Despite anumber of investigations (Bohler, 1981; Bourbaki, 1989; Calladine, 1988; Carrier, 1953; Cole, 1994; Eckhaus, 1994; Frenkel, 1996; Grebennikov and Ryabov, 1975; Kirchraber, 1994; O’Malley, 1993; Roseveare, 1982; Tomilova, 1990; Tzykalo, 1988; Van der Pol, 1960; Van Dyke, 1994; Verhulst, 1984; Vorontsov-Vel’yaminov, 1985; Yushkevich, 1982), asymptotic methods in many respects are still waiting for their historians. In this respect the difficulties are caused first of all by the fact that many ideas were developed simultaneously by different scientists. For instance, for the method of averaging, it is necessary to note contributions by L. Euler, J.-L. Lagrange, P.-S. Laplace, A.-C. Clairaut, C.F. Gauss, K.G.J. Jacobi, J. Hill, C. Delone, J.-H. Poincaré, B. van der Pol, U.J.J. Le Verrier, L.I. Mandelshtam, N.D. Papaleksi, N.M. Krylov, N.N. Bogoliubov, and others. We are only going to trace some of the stages of development of this method.

The zoologists claim that the embryonic evolution of an animaI

summarizes briefly the history of his ancestors during

different geological eras. Th e teacher must instruct the

children to go through the stages which were gone

through by his ancestors, to go through more quickly,

but not omitting the intermediate stages. In this sense

the history of science must be our first guide. The best

method to foresee the future development of mathematical

sciences is to study the history and modern condition

of these sciences.

—Jules-Henr i Poincaré¹