The mathematical physics equation is used to describe the states of various physical fields in the continuous distributed space and physical processes. Because mathematical physics equations are the partial differential equations which contain multiple variables. They are different to solve，then many innovative ideas are emerged in the history of the solution. This paper discusses the ways of thinking when methods such as separation of variables，infinite series and Sturm-Liouville theory were established based on the historical facts. Learning about the formation process of these innovative ideas can enlighten the study of mathematical physics equations.