The most important contribution of Pythagoras school is that they discovered irrational numbers. According to Pythagoras theorem, the diagonal length of a square with a side length of 1 should be 2, and 2 cannot be expressed by the numbers (natural numbers and fractions) they knew at that time. So they were terrified, because it violated their creed that "everything can be expressed by numbers", and they even threw hippasus, a disciple who found this number, into the sea to cover up the secret of finding an incalculable number. The discovery of irrational numbers eventually led to the first mathematical crisis in the history of mathematics, but the truth can never be erased. People finally recognized the existence of irrational numbers, which expanded the number system from rational numbers to real numbers.