The Importance of Useful Mathematics: On Tools for Its Popularization, from Industry to Art

Written popularization of mathematical sciences may have had its roots in Euler’s “Lettres à une Princesse d’Allemagne”, but have seen during the last decades an enormous increase of publications in newspapers, magazines and books. In this article we review some issues arising from our direct experience, on one hand, related to the connections of mathematics and art in the recreation of a virtual exhibition in Portugal during the WMY2000 and, on the other hand, in relation with a series of popularization articles for the magazine of the Portuguese engineering association. Concerning written popularization, we provide examples such as a natural logistic problem leading to optimization of functions without derivatives with counterintuitive results and to the use of check digit identification schemes in ID cards and in Euro banknotes, which correspond to mathematical problems with a “useful” nature or directly tangible meaning with a significant success of social communication. Illustrating the recent impact of elliptic curves in cryptography we describe the origin and the making of a recent short digital movie of mathematics and art, promoted by the “Centro Internacional de Matemática”, in collaboration with “Imaginary”.