1, hippasus (about 470 BC Mitterrand) found that the hypotenuse of an isosceles right triangle with waist 1 (that is, the square root of 2) could never be expressed by the simplest integer ratio (incommensurable ratio), thus discovering the first irrational number and overthrowing Pythagoras' famous theory.

2. The rationality of calculus is seriously questioned, which almost subverts the whole calculus theory.

3. Russell Paradox: S is composed of all elements that do not belong to itself. Does s belong to s? In layman's terms, one day Xiaoming said, "I'm lying!" "Ask xiao Ming is lying or telling the truth. The terrible thing about Russell's paradox is that it doesn't involve the profound knowledge of sets like the maximum ordinal paradox or the maximum cardinal paradox. It is simple, but it can easily destroy set theory.