brief history
Geometry has a long history. The oldest Euclidean geometry is based on a set of postulates and definitions. On the basis of postulate, people use basic logical reasoning to construct a series of propositions. It can be said that The Elements of Geometry is the first example of axiomatic system, which has a far-reaching impact on the development of western mathematical thought.
One thousand years later, Descartes introduced coordinates into geometry in Methodology Appendix Geometry, which brought revolutionary progress. From then on, geometric problems can be expressed in algebraic form. In fact, the algebra of geometric problems is an amazing method in the history of Chinese mathematics. Due to the lack of research on the history of mathematical communication between the East and the West, it is unknown whether Descartes' creation is influenced by oriental mathematics.
The fifth postulate of Euclid geometry, because it is self-evident, has attracted the attention of mathematicians of all ages. Finally, Lobachevsky and Riemann established two kinds of non-Euclidean geometry.
The modernization of geometry is attributed to Klein, Hilbert and others. Under the influence of Pluck, Klein applied the viewpoint of group theory and regarded geometric transformation as a transformation group under the constraint of specific invariants. Hilbert laid a real foundation of scientific axioms for geometry. It should be pointed out that the axiomatization of geometry has far-reaching influence and plays an extremely important leading role in the rigor of the whole mathematics. Its enlightenment to mathematical logicians is also quite profound.