In the history of mathematics development, there are many contradictions, big and small, but few can threaten the whole basic theory of mathematics and even cause crisis. Even people's doubts about the fifth postulate of Euclid's axiom of geometry for thousands of years did not cause a mathematical crisis, and eventually Luo Barczewski geometry and Riemann geometry were achieved. There have been three mathematical crises in the history of mathematics, each time because of the discovery of paradox, which deeply and widely affected the mathematical foundation.

In the 5th century BC, the cognition of mathematics was still in the early stage of forming the concept of rational number from the concept of natural number, and we knew nothing about the concept of irrational number. Early mathematics knowledge contains a lot of empirical things. At that time, people thought that all quantities could be expressed by rational numbers, especially the Pythagorean school, which believed that "everything is a number" and that the harmony between numbers is the origin of everything, and all phenomena in the universe can be attributed to integers or integer ratios.

Under this background, hippasus of Pythagoras School found that the right angle and hypotenuse of isosceles right triangle were incommensurable, which directly challenged the creed of Pythagoras School, impacted the mathematical cognition of ancient Greeks, caused people's panic and caused the first mathematical crisis.

Pythagoras School threw hippasus, who discovered the truth, into the sea in order to safeguard the "truth". It seems that Europeans have inherited this, and poor Bruno and Copernicus have also become victims. However, this great discovery did not disappear because of the death of the discoverer, but spread widely, causing people's concern and thinking. Under this pressure, Pythagoras school was forced to accept the paradox and gave the concept of list in an attempt to solve the paradox.

The concept of a monad is a very small unit of measurement, which itself is unmeasurable. Based on the list, Zhi Nuo has something to say. He thinks the list is either 0 or not. If it is 0, infinite lists can't add up to produce a length. If it is not 0, an infinite number of lists can form a finite line segment. So Zeno's paradox is also listed as part of the first crisis of mathematics.