Everyone who has studied mathematics knows that it has a branch called "geometry", but he doesn't necessarily know how the name "geometry" came from. In ancient China, this branch of mathematics was called metaphysics instead of geometry. The word "geometry" is not a proper mathematical term in Chinese, but a function word, meaning "how much".
For example, during the Three Kingdoms period, Cao Cao's famous sentence "Although I return to life" has two sentences: "When drinking, what is life like?" What does "geometry" mean here? So, who first used the word "geometry" as a technical term of mathematics and used it to refer to this branch of mathematics? This is Xu Guangqi, an outstanding scientist in the late Ming Dynasty.
Geometry has a long history. The oldest [[Euclidean geometry]] is based on a set of postulates and definitions, and people use basic logical reasoning to construct a series of propositions on the basis of postulates. It can be said that [[Geometric Elements]] is the first example of axiomatic system, which has a far-reaching influence on the development of western mathematical thought.
A thousand years later, [[Descartes]] introduced [[coordinates]] into geometry in the appendix of [[methodology]], which brought revolutionary progress. From then on, geometric problems can be expressed in the form of [[algebra]]. In fact, the algebra of geometric problems is an amazing method in [[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.