A mathematical model is a simplified description of a process. The point is not to capture everything, but to capture enough to explain, predict, or compare behavior.
Good models make assumptions explicit. That is why they are useful in science and engineering: once assumptions are visible, we can test whether they are reasonable, when they fail, and how the conclusions should be interpreted.
A quick checklist
- What is being simplified?
- Which variables matter most?
- What is ignored?
- What would make the model break?