Nine Chapters of Arithmetic and Elements of Geometry are two important works of ancient mathematics in the East and the West, which have their own characteristics in thinking methods, thus forming different styles of mathematics in the East and the West.

Nine Chapters Arithmetic is extremely rich in content, which is the sum total of mathematical knowledge accumulated in all aspects of social production and development from the Spring and Autumn Period to the Qin and Han Dynasties. The characteristics of his thinking method are mainly reflected in three aspects: first, an open inductive system, that is, by observing and analyzing specific problems, general laws and principles are summarized; The second is the content of the algorithm, that is, giving specific solutions and steps to various mathematical problems; The third is modeling method, which describes and solves practical problems by establishing mathematical models.

Compared with the nine chapters of arithmetic, Geometry Elements shows a completely different way of thinking. It is a mathematical work famous for its preciseness, and its thinking method is mainly reflected in three aspects: first, it is a closed deductive system, that is, starting from some self-evident basic axioms, various theorems and propositions are obtained through logical reasoning; The second is abstract content, that is, abstract thinking about geometric figures, ignoring their specific shapes and sizes; The third is the axiomatic method, that is, defining and standardizing mathematical concepts and operations through axioms.

Generally speaking, Nine Chapters Arithmetic and Geometry Elements have their own advantages in thinking methods, forming different styles of mathematics in the East and the West. Nine Chapters Arithmetic embodies the practicality and intuition of ancient mathematics in China with its rich contents and practical methods. The Elements of Geometry shows the theoretical and systematic nature of western mathematics with its strict logic and abstract ideas. These two works are both important heritages in the history of world mathematics, which have had a far-reaching impact on later generations.