Mathematics as an organized, independent and rational discipline did not exist before the advent of classical Greek scholars between 600 and 300 BC. To use an analogy: the Egyptians and Babylonians were crude carpenters, while the Greeks were master builders. The Greeks were second to none in the history of civilization and supreme in the history of mathematics. Its civilization lasted until about 600 AD. This period is historically known as the classical mathematics period, and the essence of its mathematical achievements are Euclid's "Elements" and Apollonius's (Conic Sections) .
The development of mathematics in Greece had profound social reasons. For example, Greece was a neighbor of Babylon and Egypt. As a slave society, it underwent a series of changes earlier. In addition, around 775 BC, Greece implemented writing reforms.
Multiple schools of mathematics were formed in ancient Greece, the more representative ones are: the Ionian school founded by Thales, the Pygotras school founded by Pygotras, the Pseudo-Apologetic school, the Eleian school, the Platonic school, etc. Etc., various schools of thought have accumulated a lot of mathematical knowledge, but none has formed a relatively complete system. By the Alexandrian period (400 BC to 641 AD) , Greek mathematicians, inspired by Plato's geometric ideas, began to systematize mathematical knowledge. Organize it, make it separate from philosophy and become an independent discipline, transition from empirical science established through experiments and observations to deductive science, and systematically introduce logical proof into mathematics. The person who completed this epoch-making work was the great mathematician Euclid. His famous book "Elements of Geometry" ushered in a new era of mathematical development and formed a system of elementary mathematics. Archimedes is one of the greatest mathematicians in the history of mathematics. His works cover a wide range of areas. Most of the works that have been preserved are geometric works, and some works on mechanics and calculation. In these studies, Not only did he have a profound knowledge of all previous discoveries in mathematics, but he also foresaw the concept of minimal division (method of exhaustion) , which played an important role in seventeenth-century mathematics. Apollonius's Theory of Conics had a profound impact on the development of geometry and dominated the mathematical world for nearly 2000 years. It was not until the Descartes era in the 17th century that fundamental changes began.
The geometry we study in middle school today is Euclidean geometry. The contribution of the Greeks to the content of mathematics - plane geometry and solid geometry, plane and spherical trigonometry, the beginning of number theory, the promotion of arithmetic and algebra by the Babylonians and Egyptians - is huge. The most significant contribution of the Greeks to mathematics is their persistence. All mathematical results must be derived by deduction based on clearly defined axioms. In terms of understanding the natural world, the Greeks began to form a rational point of view. Pygotras and Plato believed that the reality hidden under the ever-changing phenomena of nature is represented by mathematics, and believed that everything in the world Everything that happens is strictly determined by mathematical laws. Only through mathematics can we understand the essence of the physical world. Greek civilization lasted until it was finally destroyed by the Muslims in 640 AD.
