Levels of mathematical abstraction

As far as the depth of mathematical abstraction is concerned, it can be divided into three levels:

(1) Grasping the essence of things, simplifying and organizing complex problems and being able to express them clearly, we call it the simplification stage.

(2) Remove the specific content and use concepts, figures, symbols and relationships to express a class of things, including things that have been simplified, which is called the symbol stage.

(3) Establishing rules, patterns or models through assumptions and reasoning, and being able to explain specific things in a general sense, we call it the cosmic stage.

Professor Xu Lizhi also analyzed the epistemological significance of the level of mathematical abstraction, and creatively put forward the concept of "the level of mathematical abstraction" to quantitatively describe the level of mathematical abstraction.