1. Understanding concepts: The concepts and theories in advanced mathematics seem abstract and complicated, but once understood, you will find that they are actually very elegant and beautiful. For example, the concept of limit in calculus reveals the relationship between infinitesimal and infinity, which is a common phenomenon in nature.

2. Problem solving: Advanced mathematics provides a set of powerful tools and methods to solve practical problems. For example, linear algebra can be used for image processing and machine learning, and probability theory and statistics can be used for data analysis and prediction. When you see the application of these mathematical theories in real life, you will feel the beauty of mathematics.

3. Exploring the unknown: Advanced mathematics is the cornerstone of science and can help us understand and describe the world. For example, Einstein's theory of relativity is based on complex mathematical theories. When you see how mathematicians explore the mysteries of the universe through mathematics, you will feel the beauty of mathematics.

4. Appreciate formal beauty: Many theorems and formulas in advanced mathematics have beautiful forms, such as Pythagorean theorem and Euler formula. These formal beauties are not only amazing, but also stimulate our creativity.

5. Feel the beauty of logic: Mathematics is a rigorous logic system, and the reasoning process is clear and accurate. When you participate in this rigorous thinking process, you will feel the beauty of logic.

6. Enjoy the fun of thinking: Advanced mathematics requires in-depth thinking and repeated practice, which is a pleasure in itself. When you are solving a difficult problem, you may feel excited and satisfied. This is the beauty of mathematics.