A mathematical model is a quantitative description of a system using mathematical concepts and language. It is the process of creating a mathematical representation of a real-world scenario to make a prediction or provide insight. Mathematical models are used in various fields such as applied mathematics, natural sciences (physics, biology, earth science, chemistry), engineering disciplines (computer science, electrical engineering), and social sciences (economics, psychology, sociology, political science).

Mathematical modeling can be thought of as an iterative process made up of the following components:

• Identify the problem
• Do the math
• Analyze and assess the solution

Elements of a mathematical model can take many forms, including dynamical systems, statistical models, differential equations, or game theoretic models. These and other types of models can overlap, with a given model involving a variety of abstract structures. In general, mathematical models may include logical models.

Mathematical modeling can help to explain a system and to study the effects of different components, and to make predictions about behavior. It can be used to solve problems in business or military operations, and is a large part of the field of operations research.