This essay aims to advance the debate on the conceptualization of interdisciplinarity in mathematics education by presenting the idea of the border as a dynamic semiotic cross-cultural space. We refer to three theories, that originate in different research fields and use specific languages: De Luca Picione and Valsiner's idea of the border as a metaphor, Lotman's idea of the semiosphere, and Habermas's construct of rationality. An interdisciplinary activity with high school students based on Ceva's theorem is analysed to show how the complementarity of these theories can provide a key to characterize interdisciplinarity in mathematics education as semiotic mediation among different cultures and as a comparison among rationalities. We conclude with possible developments to shed light on the educational potential of interdisciplinary activities in emerging fields.