The first mathematical crisis shows that some truths of geometry have nothing to do with arithmetic, and geometric quantities cannot be completely expressed by integers and their ratios. On the contrary, numbers can be represented by geometric quantities. The lofty position of integers has been challenged, and the mathematical views of ancient Greece have been greatly impacted. As a result, geometry began to occupy a special position in Greek mathematics. At the same time, it also reflects that intuition and experience are not necessarily reliable, but reasoning proves to be reliable. From then on, the Greeks set out from the axiom of "self-evident" and established a geometric system through deductive reasoning. This is a revolution in mathematical thought and a natural product of the first mathematical crisis.

Looking back on all kinds of mathematics before this, it is nothing more than "calculation", that is, providing algorithms. Even in ancient Greece, mathematics was applied to practical problems from reality. For example, Thales predicted the solar eclipse, calculated the height of the pyramid through shadows, and measured the offshore distance of ships. All belong to the category of computing technology. As for Egypt, Babylonia, China, Indian and other countries, mathematics has not experienced such a crisis and revolution, and it will continue to take the road of calculation and use. However, due to the occurrence and solution of the first mathematical crisis, Greek mathematics embarked on a completely different development path, forming the axiomatic system of Euclid's Elements of Geometry and Aristotle's logical system, which made another outstanding contribution to world mathematics. According to historical records, ancient Greece and China discovered irrational numbers very early. However, the theory of irrational numbers was understood and developed by the East and the West in different ways: the Greeks focused on the length relationship of geometric quantities and discussed it by logical methods from the geometric point of view of incommensurability of line segments; People in China pay attention to the practical application of digital operation, and understand and establish its rules through calculation methods from the endless calculation process.

But since then, the Greeks have regarded geometry as the basis of all mathematics, and attached the study of numbers to the study of shapes, thus separating the close relationship between them. The biggest misfortune of doing this is to give up the study of irrational numbers themselves, which greatly limits the development of arithmetic and algebra, and the basic theory is very thin. This abnormal development trend has lasted for more than 2000 years in Europe.