Why Hidden Assumptions Undermine Every Mathematical Model

I often emphasize that mathematical modeling places great importance on “assumptions,” which both simplify problems and serve as the premise for subsequent reasoning.

In real life, many discussions start without clear assumptions; people debate and judge without clarifying basic premises, leading to contradictory and vague conclusions.

For example, when asked “In an economic downturn, should consumption be reduced?” different answers arise because each person holds a different “default assumption”:

Assume future income will decline, so be cautious.

Assume current consumption can stimulate the economy, a positive signal.

Assume the government will provide subsidies, keeping household consumption stable.

Make no assumption, just follow inertia.

This implicit “premise assumption” underlies all judgments and model construction. The problem is that we often are unaware we are speaking based on assumptions, making it hard to assess a model’s reliability and applicability.

Even when we list a few assumptions, we must ask whether they are sufficient as model assumptions.

Close your eyes, ignore the model, and consider whether these assumptions can “naturally” lead to that model structure.

In other words, I try to hide the model first, then derive from existing assumptions and logical mechanisms what the model should look like. If I cannot derive the current model, it indicates a logical mismatch between assumptions and structure, requiring revised assumptions or a different model.

Simple summary:

Recognize that models rest on assumptions and state them as clearly as possible.

Validate the match between assumptions and the model; if mismatched, refine assumptions or adjust the model.