Problem posing is not only a powerful driving force for the development of mathematics but also an incubator for the emergence of new techniques and theories. In this chapter, four significant problems from the history of mathematics have been selected as case studies to analyze how mathematicians pose problems. As shown by literature analysis results, the abstraction of real-world or physical problems, inductive reasoning from finite observations, analogies among different mathematical objects, and reflection on the results and methods of problem solving are the basic ways for mathematicians to pose problems.