On the Non-Universality in Mathematical Language

The authors analyze examples of the manifestation of non-universality in mathematical language. The identified inconsistencies are due to both cultural differences between national mathematical schools and differences in approaches in different scientific schools, regardless of their cultural background. Currently, university teachers of math pay insufficient attention to analysis of inconsistencies. At the same time, the formation of students' competencies in this area will ensure their successful professional communication in international environment in future. Authors split the analysis results into four groups. The first group includes discrepancies in Russian and English concepts describing various mathematical categories. Knowledge of these inconsistencies greatly simplifies the professional communication of mathematicians in the international aspect. The second group includes differences in the designation of “nominal” mathematical objects in Russian, English, French and German. These discrepancies are not critical in intercultural communication, because the correspondence is easily established based on graphs and formulas. The authors form the third group of inconsistencies between Russian and English mathematical terminology arising due to cultural differences in the development of math sections in scientific schools in different countries. In this case, establishing correspondences requires a lot of effort, since there are no equivalents for a number of terms, while others differ due to differences in approaches to their justification. Accordingly, teachers should pay special attention to the formation of intercultural competencies of students in this area. Finally, the fourth group includes inconsistencies in the interpretation of some mathematical phenomena, both in Russian and in English, resulting from variations in the approaches of various scientific schools. The authors give two striking examples from Probability Theory. Students' awareness of these differences undoubtedly contributes to the development of their critical thinking and cognitive abilities in general.