Geometry plays an important role in mathematical research. First of all, geometry is a subject that studies the relationship between space shape, size and position, and provides a foundation and framework for other branches of mathematics. For example, algebraic geometry studies the relationship between polynomial equations and geometric objects, while topology focuses on the continuity and connectivity of space.

Secondly, geometry is also widely used in physics, engineering and computer science. For example, in physics, geometry is used to describe the motion trajectory of objects and the way of force action; In engineering, geometry is used to design and analyze building structure, circuit layout and so on. In computer science, geometry is used to process data such as images, graphics and three-dimensional models.

In addition, geometry also involves many profound and interesting problems, such as the four-color theorem and Fermat's last theorem. These problems not only stimulate the interest and creativity of mathematicians, but also provide inspiration and reference for the development of other disciplines.

In a word, the importance of geometry in mathematical research is self-evident. It is a bridge connecting different branches of mathematics and an important tool to solve practical problems. With the continuous development of science and technology, the application prospect of geometry will be more and more broad.