Although mathematics has appeared for thousands of years before ancient Greece (even longer if primitive people are counted), it belongs to empirical mathematics, and it was not until ancient Greek mathematics developed into deductive mathematics. As an independent knowledge system, mathematics originated in ancient Greece. Since its birth, mathematicians have been pursuing the truth for more than 2,000 years, and the highest achievement of brilliant ancient Greek mathematics is embodied in Euclid's immortal work The Elements of Geometry in Alexandria.

The Pythagorean school (about 560 BC ~ 480 BC) and the wise school made outstanding contributions to mathematics in Athens. The most famous achievements of the former are the proof of Pythagorean Theorem (called Pythagorean Theorem in the West) and the discovery of irrational number root number 2; The latter put forward three famous geometric drawing problems, which attracted countless mathematicians at that time and later to study hard. It was not until modern times that these pictures proved impossible. However, mathematicians have made many theoretical achievements in the research process, such as the discovery of quadratic curve and the mathematical proof of exhaustive method.

The highest achievement of ancient Greek mathematics is embodied in Euclid's immortal work "Elements of Geometry" in Alexandria (about 323 ~ 235 BC). This book systematically sorts out and summarizes the mathematical achievements of predecessors by axiomatic method, that is, starting from several simple axioms, 467 theorems are deduced through strict deductive logic, thus forming a complete theoretical system of elementary geometry knowledge. The Elements of Geometry played an important role in demonstrating the development of ancient Greek science and later western learning. The conic curve written by Apolloni (about 262 BC-262 BC 190), who was contemporary with Euclid, was also an outstanding mathematical work in ancient Greece. He used a plane truncated cone to get all kinds of quadratic curves. Ellipse, parabola and hyperbola were all named by him. There are some structural defects in the Elements of Geometry, but this does not detract from the lofty value of this work. Its far-reaching influence makes "Euclid" and "geometry" almost synonymous. It embodies the mathematical thought and spirit laid by Greek mathematics and is a treasure in human cultural heritage.

At the same time, Archimedes (about 287 BC ~ 2 BC12 years) worked out the method of finding the area and volume of sphere, the area of arch and the area surrounded by parabola and spiral. He solved many difficult problems by exhaustive method, and also solved the quadratic equation of one variable by conic method.