Technological Innovation and New Mathematics: van der Pol and the Birth of Nonlinear Dynamics

Abstract

It is sometimes claimed that the emergence of a form of mathematization of phenomena based on the use of nonlinear mathematical models resulted from (or was at least favoured by) the needs of 1940s technology, in particular during World War II. There is no doubt that the introduction of a large number of new applications or indeed of new branches of mathematics was a response to the wartime situation. The period that began in the 1940s saw the development of game theory, linear and nonlinear programming, cybernetics, the science of digital calculus, information theory, and nonlinear dynamics. It is equally well known that the notions of feedback and servomechanism played a central role in some of these developments, which thus seem to be closely related to a profound change in technological conceptions. It would however be somewhat superficial to overlook the fact that the roots of these developments originate in the earlier past, in particular in the case of nonlinear modelling and the analysis of feedback processes.