Why Defining the Right Problem Is the First Step in Mathematical Modeling

Mathematical modeling is a way of thinking and solving problems, though it is not the only way.

The premise of solving a problem is that a problem exists; without posing a problem there is nothing to solve, so we stress the ability to formulate problems.

To whom do we pose the question? What kind of problem are we solving?

We ask the situation, aiming to solve an important aspect of that situation.

Ultimately, we must clearly see what the situation is: it contains people, objects, goals, expectations, emotions, and feelings. Different individuals in the same situation focus on different aspects, leading to many possible questions. The situation itself is objective, while each person's view is subjective.

Let the problem be ___, the situation be ___, the person be ___; expressed in functional form this can be written as ...

It can also be expressed probabilistically, representing a probability, so the question we pose corresponds to a conditional probability.

Imagine a scenario where a math teacher introduces the concept of functions to the whole class, gives examples, and then asks: "Students, can you propose a real‑life question about functions?"

What will the students answer? Feel free to comment.