Good Mathematical Modeling

Sitting in a program committee meeting as I write this...

I interpret mathematical modeling as the act of representing a "real" system through a mathematical formulation, for purposes of both quantitative and qualitative insights--into design, operation, and performance. One of the key features of good models is that they retain enough connection to the system to make the qualitative insights robust, and yet remain parsimonious enough mathematically to be tractable. I am thus often surprised that the reaction to good modeling papers is to claim, "But they didn't include Feature X of the system!" Now, if Feature X is necessary to have a robust model, then this is a fair claim. But often, Feature X is an orthogonal feature, that only adds extraneous detail and complexity to an otherwise elegant system representation. As an advisor of mine once said, the best work is done at the boundary between the trivial and the intractable; I say kudos to those who walk this line successfully.