We will define Environmental Science to so that it correspond to popular notions of environmental `problems' like climate-change, land-degradation and air or water pollution. It is inter-disciplinary and willing to address the messiness and clutter of the real world. Its motivation is often practical and immediate; we usually want to predict the consequences of altering our environment in some way.

Such prediction involves solving differential equations. These involve the rates of change of things in time and space. Solving them yields the spatial or temporal variability of the thing that we are trying to predict, which is often the probability of some event. It is in the process of choosing the differential equations, and testing the quality of the solution, that Environmental Science may be departing from the 300-year tradition of natural science.

The environmental scientist is more likely to talk of building a mathematical model of some environmental system than of proposing a theory. Complexity of this model reflects the uncooperative complexity of the real world. Penetrating insights offered by abstraction, idealisation and analytic treatment are becoming rare. Instead of `proving a theory' he talks of `validating a model', which often can go no further than ensuring that the statistics of the model output and the prototype situation match-up, to a certain degree.

What room is there then, in this enterprise, for the traditional rôle of mathematics as extending and leading physical understanding? There is indeed lots of room; but a more critical spirit needs to be injected into modelling if Environmental Science, as we have here defined it, is to receive the full benefits available from mathematics.

1/28/1997