“What is Mathematics?” and why we should ask, where one should experience and learn that, and how to teach it

Abstract

“What is Mathematics?” [with a question mark!] is the title of a famous book by Courant and Robbins, first published in 1941, which does not answer the question. The question is, however, essential: The public image of the subject (of the science, and of the profession) is not only relevant for the support and funding it can get, but it is also crucial for the talent it manages to attract—and thus ultimately determines what mathematics can achieve, as a science, as a part of human culture, but also as a substantial component of economy and technology. In this lecture we thus • discuss the image of mathematics (where “image” might be taken literally!), • sketch a multi-facetted answer to the question “What is Mathematics?,” • stress the importance of learning “What is Mathematics” in view of Klein’s “double discontinuity” in mathematics teacher education, • present the “Panorama project” as our response to this challenge, • stress the importance of telling stories in addition to teaching mathematics, and finally, • suggest that the mathematics curricula at schools and at universities should correspondingly have space and time for at least three different subjects called Mathematics. This