Running hither and thither over the last few months, trying to keep up with the demands of next spring's RAE, the perennial influences of Foresight, and of the shrinking overall science research budget has left little time for some of us (and me in particular) to sit back and contemplate the significance for research in mathematics of these rapid and major changes of climate.
The realisation that a comment column was due next morning concentrated the mind wonderfully, and the upshot is that I find myself more optimistic than I had expected. I am reminded of the old chestnut about optimists and pessimists; the pessimist sees a glass as half empty, the optimist as half full. The point that we in applied mathematics research must grasp is that we are either nowhere, or everywhere, depending upon our own perception and our own initiatives.
Dynamical systems has not been identified as a key topic in any Foresight programme, but the need for ``modelling'' appears frequently, and above all we are modellers. We seek and claim to aid understanding of complex situations through `simple' models, which capture essential features and mechanisms. Beloussov-Zhabotinsky, Lorenz, Fitzhugh-Nagumo, Kuramoto-Sivashinsky, and many others, exemplify the role to be played, complementary to large scale numerical simulation, and of course observation and experiment, by good mathematical models.
My message to the `nonlinear community' is to be imaginative, innovative and optimistic. Innumerable problems in all fields of physical and biological science, engineering and technology, even some of the social ``sciences'', now have the backing of firm data and underpinning hypotheses which needs the help of focused, rigorous mathematical insights. The world awaits us, let us as nonlinear dynamicists not be found wanting.
Professor J. Brindley. 4th January 1996.
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