In this paper we discuss the Socratic method from the aspects of subject education and examine the meaning of the method in mathematics education that is the most suitable subject for the realization of the Socratic method. In addition, as a realization of the Socratic method, we conducted a teaching-learning experiment of complex natural exponential function with a 2nd year college student. The results of the experiment are analyzed with the intention of improving instruction of the complex analysis that is one of the college mathematics courses.