Geometry is of great significance in the study of advanced mathematics. First of all, geometry is the basis of studying the shape and structure of space, which provides intuitive images and models for higher mathematics. Through geometric methods, we can better understand and describe complex mathematical concepts and problems, such as curves, surfaces and solids.

Secondly, geometry is closely related to the branches of mathematics such as algebra and analysis. For example, concepts such as vector space and linear transformation in linear algebra can be explained and understood by geometric methods. Concepts such as limit and derivative in calculus can also be displayed and explained intuitively through geometric figures. Therefore, geometry provides a unified framework and language for all branches of higher mathematics.

In addition, geometry also plays an important role in computer science, physics and other fields. Computer graphics, computer aided design and other fields need to use geometric knowledge to process and represent objects and scenes in three-dimensional space. Problems such as kinematics and mechanics in physics also need to be analyzed and solved by geometric methods.

In a word, geometry is of great significance in the study of advanced mathematics. It not only provides us with intuitive images and models, but also has close ties with other branches of mathematics, and plays an important role in computer science, physics and other fields.