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This is more understandable than the Wikipedia entry.

**WHAT IS MATHEMATICAL MODELING?**

Mathematical modeling is the process of creating a

mathematical representation of some phenomenon in

order to gain a better understanding of that

phenomenon. It is a process that attempts to match

observation with symbolic statement. During the

process of building a mathematical model, the modeler

will decide what factors are relevant to the problem

and what factors can be de-emphasized. Once a model

has been developed and used to answer questions, it

should be critically examined and often modified to

obtain a more accurate reflection of the observed

reality of that phenomenon. In this way, mathematical

modeling is an evolving process; as new insight is

gained, the process begins again as additional factors

are considered. “Generally the success of a model

depends on how easily it can be used and how accurate are its predictions.” (Edwards & Hamson, 1994,p.3)

What is the difference between the two?

Another explanation from Britannica.