Why Solve Your Mathematical Model? The Importance of Concrete Results

1. Why Must We Solve a Model?

Students familiar with the mathematical modeling process may wonder why solving the model is necessary; after all, if we don’t solve it, what is the point of building it? For many beginners, their reports contain analysis but no solution, which raises this question.

2. Providing Results Is the Goal of Problem Solving

Building a mathematical model clarifies key factors and translates them into symbolic variables that are easier to manipulate mathematically. A good model captures the core features of a problem and can be applied to similar cases. However, often we need to deliver a concrete result, such as “Which computer is most suitable for Teacher Wang’s modeling class?” without a specific brand or model the problem remains unsolved.

Even if many suitable options exist, presenting several scenarios or examples, or using flowcharts or decision trees, still provides actionable outcomes rather than leaving the solution to the reader.

3. Results Enable Verification

Without results, a model cannot be validated, preventing iteration and improvement. This is analogous to a student writing only the method for a homework problem without actually solving it; the answer is needed to compare against a standard and to reflect on mistakes.

In mathematical modeling, although there may be no single correct answer, obtaining a result for verification serves the same purpose as traditional problem‑solving practice.

4. Multiple Ways to Obtain Results

Sometimes solving analytically is difficult, so modelers may use computational tools, approximate solutions, or relaxed formulations to obtain satisfactory results, especially in competitions or time‑constrained situations.

In summary, a modeling solution that yields concrete results constitutes a relatively complete proposal.