"Abstraction in mathematics is the process of extracting the underlying essence of a mathematical concept, removing any dependence on real world objects with which it might originally have been connected, and generalizing it so that it has wider applications or matching among other abstract descriptions of equivalent phenomena.
Many areas of mathematics began with the study of real world problems, before the underlying rules and concepts were identified and defined as abstract structures. For example, geometry has its origins in the calculation of distances and areas in the real world; statistics has its origins in the calculation of probabilities in gambling; and algebra started with methods of solving problems in arithmetic.
Abstraction is an ongoing process in mathematics and the historical development of many mathematical topics exhibits a progression from the concrete to the abstract.
The advantages of abstraction are :
- It reveals deep connections between different areas of mathematics
- Known results in one area can suggest conjectures in a related area
- Techniques and methods from one area can be applied to prove results in a related area.
The main disadvantage of abstraction is that highly abstract concepts are more difficult to learn, and require a degree of mathematical maturity and experience before they can be assimilated.These persons we have placed in positions of economic authority simply CANNOT DO THIS... they do not possess the necessary degree of this cognitive skill.
I've heard it said that one of the WORST things a so-called "educator" can say to a student is: "How can you not understand this... IT IS SOOO EASY!... ".
An "educator" who would say something like that is perhaps not qualified to be an educator, perhaps politics would be a better field for that person to operate within.