Although research on mathematics education incorporating humor generally expects humor to improve students’ emotional experiences in mathematics learning and provides multiple ways to interpret word problems, this study examined the cognitive role of humor in authentic mathematical activities, wherein more general mathematical problems are generated from relatively particular ones. Particularly, this study clarified the cognitive role of humor in mathematics lessons that intentionally incorporate humor in secondary education. We applied the incongruity theory of humor as a theoretical framework and analyzed eighth-grade students’ mathematical activities for ascertaining the sum of interior angles of polygons. We observed that students themselves discovered that different initial assumptions led to the same mathematical conclusion. We found that the incorporation of humor into mathematics education has at least three effects, wherein humor 1) guarantees freedom of thinking in solving mathematical problems; 2) updates didactical contracts between teachers and students; and 3) enhances students’ critical thinking skills. Thus, we concluded that humor contributes to the realization of students’ authentic mathematical activities. As an implication for future mathematics education research, we point out the necessity of exploring how classroom cultures for connecting humor with mathematics might emerge.