Mathematics is a very extensive subject, and many branches of it can be considered very difficult. The following are some branches that are widely regarded as difficult in mathematics:

1. Higher mathematics branches, such as calculus, linear algebra and probability statistics, are the basis of most scientific and engineering disciplines. These branches involve complex mathematical theories and skills, which is a challenge for many students.

2. Real number analysis is an important field in mathematics, which covers the concepts of limit theory, series, continuity and calculus. It requires students to have in-depth logical reasoning and abstract thinking ability.

3. Abstract algebra involves a set of mathematical concepts, such as group theory, ring theory and domain theory. These abstract concepts and proofs require students to have basic knowledge of logical thinking and abstract algebra.

4. Number theory is a branch of studying the properties of integers, including prime numbers, integer solutions and number theory functions. It has many complicated theorems and inferences, and needs a high degree of abstract thinking and mathematical proof ability.

These branches are very important for mathematical research and application, but they are also generally considered as relatively difficult fields. However, these are subjective evaluations, because different people may have different degrees of difficulty in different branches of mathematics.