(1) Mathematical conjecture is a powerful driving force to promote the development of mathematical theory. Mathematical conjecture is one of the most active, active and positive factors in the development of mathematics and the most creative part of human reason. Mathematical conjecture can strongly attract mathematicians to join in and actively carry out related research, thus effectively promoting the development of mathematics. Once the mathematical conjecture is confirmed, it will be transformed into a theorem and integrated into the mathematical theory system, thus enriching the mathematical theory.

(2) Mathematical conjecture is an important way to create mathematical thinking methods. The history of mathematical development shows that mathematicians have created a lot of effective mathematical thinking methods in the process of trying to solve mathematical conjectures (whether they are finally solved or not). These mathematical methods have penetrated into all branches of mathematics and played an important role in mathematical research.

(3) Mathematical conjecture is a rich source of scientific methodology research. First of all, as a research model, the law of its emergence and development is an important basis for discussing the research methods of mathematical science; Secondly, as a research method, mathematical conjecture itself is the research object of mathematical methodology, which promotes the study of general principles of mathematical methodology by studying and solving the regularity of some new methods shown in mathematical conjecture; Finally, as an important form of mathematical development, mathematical conjecture is the concrete embodiment of scientific hypothesis in mathematics. It is of special value to study the types, characteristics, methods and general scientific methods of solving mathematical conjectures, especially the creative thinking methods.