Resumen

This paper discusses the generally shared conviction of mathematics being a universal science, with a “common language” and a “shared research agenda”. These convictions are discussed in particular with regard to assertions in the volume “Mathematics Unbound” of 2002, where it is maintained that national mathematical communities emerged during the 19th century but converged to a universal community during the 20th century. Emphasising the key importance of the national educational structures, it is argued here that national communities emerged already in the wake of Humanism. The differing “languages” for conceiving of negative numbers provide revealing examples for showing epistemologies related to different educational structures. And a fundamentalist “language” in Italy shows the alignment of mathematics education with classicist conceptions of education. Connecting with the conception of “national styles”, the paper proposes approaches to understand characteristics marking the differences between national mathematical communities as tied to social and cultural values and revealed by the education systems. In the conclusion, the claim of an emerged international community is discussed.