What are the three crises of numbers in the history of mathematics? You must be concise, and then concise. Other people's answers are so big that I have a big head.
First, a student found that the hypotenuse of an isosceles right triangle whose base is 1 (i.e. root number 2) can never be expressed by the simplest integer ratio, thus discovering the first irrational number and overthrowing Pythagoras' famous theory, but because of this, the student was also thrown into the sea; Secondly, the rationality of calculus is seriously questioned, which almost subverts the whole calculus theory; Third, Russell's paradox: S is composed of all elements that do not belong to itself, so does S belong to S? Generally speaking, one day Xiaoming said, "I will always lie!" " "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. Destroying set theory is simple and easy!