讀者在处理数学問題可能已經有过这样的經驗:試图直接解决一个数学問題正在一筹莫展的时候,往往是把它化成另一个等价的問題而得到解决;直接解决原問題之所以感到棘手,一方面固然可能由于原問題的确难以直接处理,另一方面也可能是由于对問題的这种表現形式以及解决它所需的知識和工具掌握得不够充分。把一个問題化为另一个等价的問題,就增大了我們已經掌握的工具和知識的利用率;問題采用不同的表現形式,就会因使用的方法不同而增大了解决它的可能性。列举出問題的一切表現形式,以便从中选出一种合适的来处理,从方法論的观点說来,这是十分重要的。本文的目的,一方面固然是介紹Hurwitz- The reader may have had such experience in dealing with mathematics problems: When trying to solve a mathematical problem directly, he is often overwhelmed by solving it to another equivalent problem and solving it; the reason why the direct solution to the original problem is thorny, Of course, it may be difficult for the original issue to be dealt with directly. On the other hand, it may also be due to insufficient understanding of this form of the problem and the knowledge and tools needed to solve it. Turning a problem into another problem of equal value increases the utilization of the tools and knowledge that we already have; problems with different forms of expression will increase the likelihood of solving them by using different methods. . It is very important to list all the manifestations of the problem in order to choose a suitable one to deal with. From a methodology point of view, this is very important. The purpose of this article, of course, is to introduce Hurwitz-