This paper summarizes the problems and the development trend of problem solving in artificial intelligence at home and abroad at present, supposes to solve the problems of automatic identification, automatic solution, similarity judgment, judging the reasonableness of the problem solving steps, puts forward the human thinking jump hypotheses for primary mathematics application problem solving: (1) There are some, not many, the process of basic abstract action, such as partition, enumeration, charts and arrangement, can not use conventional knowledge or ontology representation method to represent, the conventional knowledge representation and search space can not solve all the problems, there are some thinking jumps. (2) Existing the basic abstract action sequences to describe the thinking jumps, and the method of judging the reasonableness. For example, the situation semantic model to describe the basic action sequence of events as well as the constraint method to solve the problem of judging the reasonableness. (3) The number of types of thinking jump is limited. This paper describes the corresponding hypothesis of human thinking engineering simulation realization model for solving practical problems, several examples are given, for example, chicken and rabbits in a cage. Finally, illustrates the idea of development for next step.