1, Pythagoras School and Philosophy of Mathematics

Pythagoras school is considered as one of the representatives of ancient Greek mathematics, and its mathematical thought is closely related to philosophical thought. The Pythagorean school put forward many viewpoints and theories about the speculative nature of mathematics and philosophy, the most famous of which is "everything has a number".

2. The philosophical significance of "everything is important"

Pythagoras school believes that the essence of the world is composed of numbers, and all phenomena and things can be expressed and explained by numbers. This view was very avant-garde and groundbreaking at that time, which had a far-reaching impact on later mathematics and natural science.

3. Other mathematical philosophies of Pythagoras school.

In addition to "everything is valuable", the Pythagorean school also put forward some other important viewpoints of mathematical philosophy. For example, they believe that real knowledge can only be acquired through wisdom and reasoning, not through perceptual knowledge or belief.

Pythagoras' influence on later philosophy and science

1, its influence on philosophy

In philosophy, Pythagoras first put forward the word "philosophy", which means "love of wisdom". Calling himself and his disciples "philosophers" means "people who pursue wisdom". Distinguish between "wise men" and "fools" The former is guided by reason, while the latter is guided by senses.

It emphasizes the role of reason in understanding the world, and holds that only through reason can we grasp the real and eternal things, while the senses can only perceive the illusory and changing things. These thoughts have important inspiration for later philosophers such as Plato and Aristotle.

2, the impact on science

In science, Pythagoras regards mathematics as a kind of pure rational knowledge independent of experience, and thinks that mathematics can be used to explain natural phenomena and laws, thus establishing the basic position of mathematics in science. Mathematical theorems and music theories have made great contributions to later scientific fields such as geometry, algebra, physics and astronomy.

A cosmic model is also proposed, which holds that the planets such as the earth, the moon and the sun all revolve around a central fireball to form a harmonious music, that is, the sound of the celestial sphere. These thoughts had an important influence on later scientists such as Copernicus, Galileo and Newton.