In 430 BC, sophistry school and Plato school appeared in ancient Greece.
Sophism was the first school in Athens. This school includes various scholars and masters, such as grammar, rhetoric, dialectics, oratory, interpersonal relationship, geometry, astronomy and philosophy. The mathematical research center of sophistry is three famous geometric problems in history: (1) bisecting any angle; (2) Cube-find a cube, so that its volume is twice that of the known cube; (3) Turn a circle into a square-find a square so that its area is equal to the known circle. The difficulty of these problems lies in that the drawing tools are limited to compasses and rulers without scales. After Plato (430-349 BC) advocated it, it was included in Euclid's Elements of Geometry, which became a difficult problem affecting future generations for more than two thousand years. Until the19th century, it was developed by Wanzel (1814-1848) (1837) and Lin Deman (1852- 1939). Finally f? Klebsiella pneumoniae (F. Kiein,1849-1925) gave a concise proof of impossibility in 1895, which completely solved the unsolved case for more than 2000 years. (Note: It's a pity that there are still many young people trying to make a big splash and put their energy into the three major problems that have been solved! )
An Tifeng (about 430 BC) of the sophistry school solved the problem of "turning a circle into a square"; Put forward a valuable method, later called "exhaustive method", which is the bud of limit theory. An Tifeng's method is: first make a circle inscribed with a square, and double the number of sides to get an inscribed octagon; Double it again and get a polygon of 16. In this way, the regular polygon exhausts the circle and can always make a square with the product of the regular polygon, so that the circle can become a square.
Obviously, the conclusion of the square is wrong, but it shows people the dialectical relationship between "curve" and "straight line" and an approximate method to find the area of a circle, which inspires people to use "curve" instead of "straight line" to solve problems later. For example, Archimedes' cyclotomy is the embodiment of this idea.
After the sophistry school, Plato school led the mathematical activities. The leader of this school is Plato (about 430-349 BC). Plato was born in Athens and had a keen interest in mathematics. His philosophy is permeated with mathematical thoughts. He founded Plato's Academy in Athens, and the school gate was hung high. "Those who don't know geometry are not allowed to enter." Western scientific circles respect the tradition of mathematics; It originated from this university. Adhere to accurate definitions, clear assumptions and proofs, and train many scientists. Archimedes is one of them.
The heyday of the Athens Cultural Center lasted for more than half a century. With the decline of Athens, cultural prosperity gradually shifted from Athens to Alexandria.
The word "sophistry", originally intended to make people wise, has also been translated into "philosopher school" or "homo sapiens school", and now it has become a derogatory term "unreasonable argument" This is changed to "sophistry"