What Is Mathematical Modeling and Why It Powers Real-World Problem Solving

In simple terms, mathematical modeling is the process of solving problems using mathematical models. A mathematical model is an abstract structure composed of mathematical language (symbols, formulas, etc.). For example, Newton’s second law describing the relationship between acceleration and force is a typical mathematical model:

where F is force, m is the object's mass (kilograms), and a is acceleration (meters per second squared).

A mathematical model is similar to a tangible physical model (such as a toy car or airplane). Through a physical model we can learn characteristics of the original object. A toy car lets a child understand a real car’s appearance, key structures (wheels, chassis, body) and function (it can move), thus depicting the real car, though it is not the actual car.

Mathematical models are more abstract than physical models; they consist of a set of abstract mathematical formulas but still serve to depict phenomena. For instance, the mathematical model of Newton’s second law captures the abstract relationship between force and acceleration.

The background of mathematical modeling often comes from real life, encouraging students to use mathematical knowledge and methods to solve practical problems, stimulate interest in mathematics, and enhance their ability to address real issues. Through mathematical modeling we can gain deeper insight into real‑world problems and solve them more effectively, thereby promoting scientific, technological, and socio‑economic development. Mathematical modeling, as an interdisciplinary and comprehensive discipline, requires both mathematical knowledge and understanding of real problems, as well as creative thinking and hands‑on skills.