mathematicization

Mathematicization refers to the process of translating concepts, phenomena, or problems from a particular domain into mathematical language and frameworks. This involves identifying relevant quantities, relationships, and structures within the original domain and then representing them using mathematical objects, equations, or models. The goal is to leverage the power and rigor of mathematics to analyze, understand, and potentially solve problems that may be difficult or impossible to tackle using non-mathematical methods alone.

This process often begins with abstraction, where essential features of the real-world situation are identified and simplified. These features are then assigned mathematical counterparts. For instance, physical objects might be represented by geometric shapes, their movements by functions, and their interactions by equations. Once a mathematical model is constructed, it can be manipulated using established mathematical techniques. This might involve solving equations, performing calculations, or applying theorems. The results obtained from the mathematical analysis are then interpreted back in the context of the original domain, offering insights, predictions, or solutions.

Mathematicization is a fundamental aspect of many scientific disciplines, including physics, engineering, economics, biology, and computer science. It is also a key component of applied mathematics and operations research. The success of mathematicization depends on the degree to which the mathematical model accurately captures the essential characteristics of the phenomenon being studied and the effectiveness of the mathematical tools used to analyze the model.