There are two characteristics you have to emphasize when you turn to mathematical modelling, these characteristics referring to the object. These characteristics are informative, but they also allow you to mathematically formalize the object. The formalization involves the possibility to create a correspondence between the characteristics of the original object and adequate mathematical notions, such as numbers, functions and so on. The connections identified and the hypothetical ones can be described using mathematical relations, such as equations, inequalities, formulas and so on. The result of such a process is the mathematical model.
This model is a system of maths relations, which describe the essential properties of the original. Therefore, the solution of a real problem can be reduced to solving a mathematical problem. The mathematical symbols, especially the quantitative ones, represent one of the most common means of describing the properties of the surrounding world. A mathematical description can be tested from the point of view of the logical contradictions, of the estimation of the level of the results obtained, of the data processing and so on.
This method appeared and was developed in physics. For example, there is the mathematical model for the straight uniform movement, where D is the distance covered by the vehicle, s is its speed and t is the time registered. Then, the universal attraction law is an excellent model of the interaction between the Sun and the rest of the planets. Mathematical modelling is a creative activity, which is why it is quite complicated to describe it in a formalized way.
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