What are the original theories of several books?

If the Ionian school is the earliest physicist, then the Huadagoras school is the earliest mathematician. Their views are contrary to those of Ionians. The latter thinks that the origin is single and changeable; Pythagoras believes that number is the origin of all things, which is numerous and unchangeable. They have two main reasons:

First, the essence of everything can be summed up in the stipulation of numbers. In numbers, we can find many features similar to existing things and things produced in natural processes, more than those found in fire, soil or water. In other words, the stipulation of numbers is more common than physical attributes. A thing can lack some physical attributes, but it can't be without the stipulation of numbers. Therefore, the origin applicable to all things is not the material form (water, gas and fire) with certain physical properties, but the number. The mathematical stipulation understood by Pythagoras can be roughly divided into three categories: one is the mathematical proportional relationship, which determines the structure of things and the harmony between things; There is also an opposition in mathematics, such as finite and infinite, odd and even, one and many, straight line and curve, square and rectangle; In addition, it also includes the analogy relationship between the natural attributes and social attributes represented by numbers, such as 4 for justice and 1O for perfection; Some realistic opposites, such as left and right, yin and yang, movement, light and shade, good and evil, can also be analogized by mathematical relations.

Second, number exists before things and is the basic unit of things. Their basic idea is that all shapes have geometric structures, and the geometric structures correspond to numbers: 1 is a point, 2 is a line, 3 is a surface and 4 is a body. The generation process of the world is that points generate lines, surfaces generate lines, surfaces generate bodies, and bodies generate sensory bodies, producing four elements: water, fire, air and earth. Aristotle criticized this view for confusing abstract numerical units with physical particles with volume. This is indeed the theoretical weakness of Vadagras. Geometric figures composed of points, lines, surfaces and bodies have no physical properties, and geometric structures cannot replace the natural motion of perceivable things. Even so, Pythagoras' thinking on the geometric structure of the world is no less significant than Ionian's thinking on the process of world formation, and represents the earliest mathematicians and physicists' way of looking at the world respectively.