About the 5th century BC, hippasus of Pythagoras School found that the right side of an isosceles right triangle and its hypotenuse were incommensurable. The discovery of this incommensurable measure and Zeno's paradox together triggered the "first mathematical crisis".
Because of this mathematical discovery, hippasus was thrown into the sea by the Pythagorean school and was punished by "drowning". Because he actually created such a thing in the universe to deny the Pythagorean creed: all phenomena in the universe can be attributed to integers or the ratio of integers.
Pythagoras School is one of the oldest schools of philosophy in ancient Greece. It is said that this school has two maxims that best summarize their ideological characteristics: "What is the smartest? Only the number "What is the best"? Only harmony. " The great contribution of Pythagoras school to mathematics is to prove Pythagoras theorem, but it is also found that the hypotenuse of some right-angled triangles cannot be expressed as integers or the ratio of integers (incommensurability), such as right-angled triangles with all right-angled sides of 1.
It is found that the right side of a right triangle and its hypotenuse are not commensurable, which puzzles Pythagoras school. It not only violated the Pythagorean creed, but also impacted the belief that "all quantities can be expressed by rational numbers" held by the Greeks at that time. So people usually call this contradiction discovered by hippasus hippasus Paradox.
The discovery of this paradox shocked the western mathematics community at that time, and also caused the renewal of ancient Greek mathematics concepts. This "crisis" shows that intuition and experience are not necessarily reliable, but reasoning is reliable. From then on, the Greeks began to pay attention to from calculation to reasoning, from arithmetic to geometry, and thus established a geometric axiom system. In fact, this is a great revolution in mathematical thought!
Quoted from how the "First Mathematical Crisis" was triggered ―― On hippasus Paradox and Zeno Paradox.