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What are the similarities and differences between the views of the Greek school of mathematics, and what influence does it have on the development of mathematics and even the whole science?
In the 6th century BC, some eastern Ionian philosophers began to raise the question of the origin of the world. They oppose all kinds of myths and creationism circulated in the past and think that the origin of the world is some material elements, such as water, gas and fire. They are the earliest materialist philosophers in the west, and they use nature itself to explain the emergence of the world. The famous representatives are Thales of Miletus, anaximander, Anaximenis and Heraclitus of Afeiz. At the same time, another philosophical school with ideological tendency appeared in southern Italy. They believe that the essence of everything is not material elements, but some abstract principles. The Pythagorean school thinks that it is "number", while the Elijah school, represented by parmenides, thinks that "existence" is unchangeable and immortal, and that movement changes only the phenomenon of things. The abstract immaterial principle put forward by them has a great influence on the emergence of idealistic philosophy in the future.

What achievements did ancient Greece make in natural philosophy that had an important influence on the later scientific development?

Ancient Greek natural philosophy made an intuitive investigation of natural phenomena as a whole, and put forward many speculations of great significance to the later scientific development, which became an important ideological source of modern natural science in Europe. Mainly includes:

1, on the essence of all things in nature-elemental theory;

2. Questions about the structure of matter-atomism;

3. Cosmology, the earliest theory about celestial models.

The natural philosophy of ancient Greece is rich in content. The above-mentioned elemental theory, atomism and cosmology may not be completely correct, but it is of great significance to ask questions and think at that time. The fact of scientific development shows that the scientific thought contained in ancient Greek natural philosophy has had a far-reaching influence on later scientists.