This paper takes into consideration of the separation of 'gaku'(science) and 'jut su'(art), by examining the controversy about the Japanese for "Arithmetic" in "Yakugokai (translation committee)" of "Tokyo-sugaku-kaisya". "Yakugokai" decided "Aritmetic" should be translated into "san-jutsu" in place of "sansu-gaku". This decision has been interpreted as a result of the persuasive speeches of Dairoku Kikuchi, a professor of University of Tokyo, who claimed that "Arithmetic" was not 'gaku'as a science but 'jutsu'as an art. This paper reexamines this interpretation by illuminating the implicit efforts of traditional Japanese mathematicians, who intended to regard 'gaku'and 'jutsu'as continuous according to their traditional culture. The conflicts in "Yakugokai" resulted in the impermeable gulfs between the science of computation and the art of computation, and also between systematic knowledge in academy and learning at school in Japan.