Joyce`s intricate styles in the latter half of Ulysses sometimes brought forth misunderstandings by critics with the result that they thought Joyce was merely playing with technique for its own sake. This paper takes the "Ithaca" chapter, which is written in the form of a mathematical catechism, and attempts to argue against this perspective. In the "Ithaca" chapter, which is the penultimate chapter of Ulysses, but meant to be the closure to the plot movement, Joyce intended to tell readers about the struggle of characters who tried to break free from the bondage or nightmare of the past history. Joyce shows that it is a very heroic gesture but a very difficult task, so characters are not to blame because human beings are destined to fail. The technique of catechism is meant to show this to readers, and the chapter "Ithaca" requires this technique. In order to show the above point, this paper takes the following steps. First, it argues that the technique of mathematical catechism in "Ithaca" derives from Catholic catechism and that it is closely related to Joyce`s own aesthetic theory, according to which the ultimate goal of art is to show the quidditas of society. Second, it will explicate in detail how Joyce executes the precepts of hisown aesthetic theory in the "Ithaca" chapter, and show that Joyce succeeded in showing the quidditas of society by juxtaposing opposite emotions of comedy and sympathy. Joyce used the technique of mathematical catechism comically in "Ithaca" in order to show the struggle and the shortcomings of a modern man in achieving the goal. However, at the same time, the very comical use of catechism heightens the characters` humanity, and leads readers to sympathize with their fallen condition. Through the conflict and suspension of opposite emotions, we the readers can establish a balanced view of the characters and achieve stasis. With stasis, we can see and contemplate and realize the what-ness of a modern man, a victim predestined by his time and space.