1. Certainty: Mathematical theorem is a statement of certainty, which will not change with the change of environment. This certainty enables us to trust mathematics and use it to solve practical problems.
2. Logic: Mathematical theorems are based on logical reasoning and are conclusions derived from a series of premises. This logic enables us to understand and prove mathematical theorems, thus deeply understanding the essence of mathematics.
3. Universality: Mathematical theorems are usually universal, that is, they are applicable to all situations that meet specific conditions. This universality enables us to apply mathematical theorems to various problems and get general solutions.
4. Abstraction: Mathematical theorems are usually abstract, and they do not depend on specific values or objects. This abstraction enables us to extract general laws and principles from specific problems, so as to gain a deeper understanding.
5. Innovation: The discovery and proof of mathematical theorems often require innovative thinking and methods. This innovation makes mathematics develop and progress continuously, thus promoting the progress of science and technology.
Generally speaking, mathematical theorems are the basis of mathematical research and an important tool for us to understand and apply mathematics. Without mathematical theorems, it is impossible to carry out effective mathematical research and solve practical problems.