We should deeply understand the duality of mathematics.

First, mathematics is deductive and inductive.

Generally speaking, people know the objective world in two ways. One is to know the individual and special things, and then know the general things. This is called induction. The second is to know the special and individual things from the general things.

Law is called deduction. The deepening of understanding is realized in the alternating process of induction and deduction. Induction comes down to understanding the special properties of a class of things. Deduction takes the general conclusion as the basis of studying others.

So induction is the basis of deduction, and deduction is the deepening of induction.

The Elements of Geometry is the first theoretical monument in the history of mathematics development. Euclid combed and refined the original mathematical knowledge, established the starting point of the theory on human intuition, and found several most intuitive original concepts, postulates and axioms, relying on human thinking.

Based on the advanced logical reasoning model, the propositions after the performance are deduced one by one, and the plane geometry theory is constructed by using the deductive system, thus the axiomatic thought and deductive reasoning paradigm are established. People's admiration for mathematical deduction system expresses their absolute belief in scientific theory and method.

Since then, mathematics has entered the smooth road of development.

Axiom system makes mathematics have distinct subject characteristics, clear logical starting point, clear concept and correct judgment. Deductive reasoning makes mathematics clear, solid and correct, thus showing great power. Deduction can lead to induction, when deduction

When reasoning is blocked, it is to ask questions to induction, which urges induction to transcend vagueness, fragmentation and incompleteness.

The theoretical system constructed by logical deduction limits the freedom of thinking, because the system is mostly the repetition of the same language, which can only be circulated and cannot be advanced. This is an important reason why European geometry theory has become a long-term obstacle to non-European geometry. Thus, logical deduction

Its main function is not to discover new conclusions, but to construct the inevitable relationship among basic concepts, basic operations and basic propositions. Logical deduction is good at checking whether the path between these connections is effective, but it is difficult to determine whether the path points in the right direction because it determines the right direction.

The way is to make a choice, and this is precisely the power of induction.