The essence of mathematics: what it is, for what and what it is to do with?

A profound understanding of the essence of mathematics is the foundation for a teacher’s flexible control of mathematics teaching, which is of fundamental guiding significance for teachers to carry out mathematics teaching. It has an important realistic significance to have a thorough examination of "the essence of mathematics", "why it is necessary to implement the teaching highlighting the essence of mathematics" and "how to implement the teaching highlighting the essence of mathematics". Based on the plural essence view of mathematics, five principles are put forth for the implementatation of the teaching that highlights the essence of mathematics: "equal importance placed on phenomenon and essence, form and content, process and result,absolutism and fallibilism, sensibility and rationality".