Leigh Tesfatsion concludes her paper (Agent-based Computational Economics: A constructive approach to Economic Theory, 2006, in the Handbook of Computational Economics) beautifully summing up how I feel about the subject and approach:
As a professor of mathematics (as well as economics), I appreciate the beauty of classical mathematics. However, constructive mathematics is also beautiful and, in my opinion, the right kind of mathematics for economists and other social scientists. Constructive mathematics differs from classical mathematics in its strict interpretation of the phrase “there exists” to mean “one can construct.” Constructive proofs are algorithms that can, in principle, be recast as computer programs. To master a general programming language is to acquire a form of mathematical skill every bit as aesthetically pleasing, powerful, and practical as the differential calculus. Indeed, for economic purposes, computer programming is in some ways more powerful in that it facilitates the modeling of complex interactive processes involving kinks, jumps, and other forms of discreteness imposed or induced by empirical constraints. Consequently, programming frees us to adapt the tool to the problem rather than the problem to the tool. Every graduate economics program should incorporate general programming language requirements. It is time.
(Emphasis mine). This is what I’m trying to do, and trying to encourage others to at least accept, but it seems an uphill battle.