In natural science, mathematics is used to model, predict and explain natural phenomena. For example, Newton's laws of motion and electromagnetic equations in physics are expressed in mathematical language. Genetics and ecology in biology also depend on mathematical models to study and predict the evolution of species and the stability of ecosystems. The chemical reaction rate and thermodynamic properties in chemistry can also be described and calculated by mathematical equations. In addition, mathematics also plays an important role in geography, astronomy and meteorology.

In social science, mathematics is used to analyze and solve social problems. Economics is one of the important fields, in which the concepts of supply and demand, market equilibrium and economic growth are all studied through mathematical models. Statistical analysis and probability theory in sociology are also widely used to study social behavior and social structure. The voting theory and political decision analysis in politics also need to use mathematical methods. In addition, mathematics also plays an important role in the fields of psychology, pedagogy and demography.

In a word, mathematics is widely used in natural science and social science. It not only helps us to understand and explain natural and social phenomena, but also provides an accurate and systematic method for scientific research.