The basic theory of mathematics comes from axioms, not intuition. Although axiom itself comes from intuition, it does not prevent some theorems in mathematics from being counterintuitive, and some seemingly intuitive theorems cannot be deduced from the existing axiom system. For example, Dai Dejin infinity and piano infinity are equivalent and can only be deduced from axiom of choice, but not from the axiomatic system without axiom of choice. If all seemingly intuitive conjectures are written as axioms at will, then the consistency of the mathematical system, that is, non-contradiction, cannot be guaranteed.