数学物理方程是描述空间连续分布的各种物理场的状态和物理过程的方程.由于数学物理方程是含有多个变量的 偏微分方程，计算比较困难，因此在求解的历程中涌现出了许多创新思想.本文在研究史实的基础上，探讨了在面对困难时，前 人创立分离变量法、无穷级数法和斯-刘理论等方法的思维方式.了解前人解决问题的过程不仅对数学物理方法的学习具有很 大的启迪作用，而且有助于培养学生的创新意识.

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.