The ancient Greeks introduced names, concepts and self-thinking into mathematics, and they began to guess how mathematics came into being very early. Although their guesses were just jotted down, they almost occupied the thinking field of guesses first. What the ancient Greeks wrote down at random became a lot of articles in the19th century, but it became an annoying cliche in the 20th century. Herodotus (484-425 BC) was the first person who began to guess. He only talks about geometry. He may not be familiar with general mathematical concepts, but he is sensitive to the exact meaning of land survey. As an anthropologist and social historian, Herodotus pointed out that the geometry of ancient Greece came from ancient Egypt. In ancient Egypt, because the land was flooded every year, people often needed to re-measure the land in order to achieve the purpose of taxation. He also said: The Greeks learned the use of the sundial from the Babylonians and divided the day into 12 hours. Herodotus' discovery was affirmed and praised. It is superficial to speculate that ordinary geometry has a glorious beginning.

Plato cares about all aspects of mathematics. In his fairy tale Fei, which is full of wonderful fantasies, he said:

The story took place in ancient Egypt's LokLatin (region), where an old fairy lived. His name is Theuth. To Seth, ibis is a divine bird. With the help of ibis, he invented numbers, calculation, geometry and astronomy, as well as board games.

Plato is often full of strange fantasies because he doesn't know whether he is Aristotle or not. Finally, he talked about mathematics in a completely conceptual language, that is, mathematics with its own development purpose. Aristotle said in chapter 1 of his Metaphysics: Mathematical science or mathematical art originated in ancient Egypt, because there were a group of priests who devoted themselves to mathematical research freely and consciously. It is doubtful whether what Aristotle said is true, but this does not affect Aristotle's intelligence and keen observation. In Aristotle's book, ancient Egypt is mentioned only to solve the argument about the following problems: 1 Knowledge serves knowledge, and pure mathematics is the best example: 2. The development of knowledge is not due to consumers' demand for shopping and luxury goods. Aristotle's "naive" view may be opposed; But it can't be refuted because there is no more convincing point of view.

Generally speaking, the ancient Greeks tried to create two "scientific" methodologies, one is ontology, and the other is their mathematics. Aristotle's logical method is somewhere between the two, and Aristotle himself thinks that his method can only be an auxiliary method in a general sense. The ontology of ancient Greece has obvious characteristics of parmenides's "existence" and is slightly influenced by Heraclitus's "rationality". The characteristics of ontology are only shown in the later translation of Stoicism and other Greek works. As an effective methodology, mathematics has gone far beyond ontology, but for some reason, the name of mathematics itself is not as loud and affirmed as "existence" and "rationality". However, the appearance of mathematical names reflects some creative characteristics of ancient Greeks. Below we will explain the origin of the term mathematics.

The word "mathematics" comes from Greek, which means something "learned or understood" or "acquired knowledge", and even has the meanings of "obtainable things" and "learnable things", that is, "knowledge gained through learning". The meanings of these mathematical names seem to be the same as those of Sanskrit cognates. Even Littre, a great dictionary editor (E.Littre was also an outstanding classical scholar at that time), included the word "mathematics" in his French dictionary (1877). The Oxford English Dictionary makes no mention of Sanskrit. In the Byzantine Greek dictionary Suidas in the 10 century, some terms such as physics, geometry and arithmetic were introduced, but the word "mathematics" was not listed directly.

The word "mathematics" has gone through a long process from expressing general knowledge to expressing mathematics specialty, which was completed in Aristotle's time, not in Plato's time. The specialization of mathematical names lies not only in its far-reaching significance, but also in the fact that only the specialization of the word "poem" in ancient Greece could rival the specialization of mathematical names at that time. The original meaning of "poem" is "something that has been made or completed", and the specialization of the word "poem" was completed in Plato's time. However, for some reason, neither the dictionary editor nor the knowledge questions involving noun specialization mentioned poetry, nor did they mention the strange similarity between poetry and mathematical name specialization. But the specialization of mathematical names has really attracted people's attention.

First of all, Aristotle put forward that the special usage of the word "mathematics" originated from Pythagoras' thought, but there is no data to show that there is similar thinking about the natural philosophy originated from Ionia. Secondly, among Ionians, only Thales (640 BC? -546) The achievement in "pure" mathematics is credible, because besides Diogenēs Laertius's brief mention, this credibility comes from a later and more direct mathematical source, that is, Proclus's comments on Euclid: but this credibility does not come from Aristotle, although he knows Thales is a "natural philosopher"; Nor did it come from the early Herodotus, although he knew that celis was a "lover" of politics and military tactics, and even predicted a solar eclipse. These may help explain why there is almost no Ionian component in Plato's system. Heraclitus (500 BC? There is a famous saying: "Everything is in motion, and things are impermanent", "People can't fall into the same river twice". This famous saying puzzled Plato, but Heraclitus was not respected by Plato like parmenides. From the perspective of methodology, parmenides's theory of matter is a strong competitor of Pythagoras mathematics compared with Heraclitus' theory of change.

For Pythagoras, mathematics is a "way of life". In fact, judging from some testimonies of Latin writer Galius in the 2nd century AD, Greek philosopher Porfiri in the 3rd century AD and Greek philosopher Iamblichus in the 4th century AD, it seems that the Pythagorean school has a "general degree course" for adults, including formal registrants and temporary registrants. Temporary members are called "observers" and full members are called "mathematicians".

The "mathematician" here only refers to a class of members, not to say that they are proficient in mathematics. The spirit of Pythagoras School is enduring. For those who are deeply attracted by Archimedes' magical inventions, Archimedes is the only unique mathematician. Theoretically speaking, Newton was a mathematician, although he was also a half physicist. The general public and journalists prefer to regard Einstein as a mathematician, although he is a thorough physicist. When roger bacon (12 14- 1292) challenged his century by advocating "ontology" close to science, he was putting science into a mathematical framework, although his accomplishments in mathematics were limited. When Descartes (65433) and Leibniz quoted a very similar concept, which became the basis of later symbolic logic, symbolic logic became a popular mathematical logic in the 20th century.

/kloc-In the 8th century, Montukra, a pioneer writer in the history of mathematics, said that he had heard the fact that the ancient Greeks first called mathematics "general knowledge". There are two explanations: one is that mathematics itself is superior to other knowledge fields; Another explanation is that mathematics, as a general subject, had a complete structure before rhetoric, dialectics, grammar and ethics. Montclair accepted the second explanation. He doesn't agree with the first explanation, because there is no proof suitable for this explanation in Proclus's comments on Euclid or in any ancient materials. However, the etymologists in the19th century preferred the first explanation, while the classical scholars in the 20th century preferred the second explanation. But we find that these two explanations are not contradictory, that is, mathematics has existed for a long time, and its superiority is unparalleled.