An Interdisciplinary Reading of Mathematics

Abstract

This research paper recapitulates the history of mathematics, which occupies itself describing processes of growth and development, whereas philosophy of mathematics is concerned with questions of justification. Both play an essential role within the educational context. However, there is a problem because genuine historical studies necessitate ever-greater particularity whereas mathematics and philosophy require generality and abstraction. The paper offers some methodological reflections about these matters together with two case studies from nineteenth century history of arithmetic and integration theory, respectively, which try to strike a balance between the directly opposed requirements.