Introduction

The word “duality” is used in modern mathematics for many different phenomena. Some of these have been recognized long ago in history, albeit under different names, such a the duality of Platonic solids in book XV of the Elements and in Kepler’s Harmonices mundi books II and V, or the polar triangle in spherical geometry. The idea became more prominent and explicit in the context of projective geometry starting around 1810, and it was in this context that the term “duality” was coined (although “reciprocity” or “polarity” were also used). With the emergence of modern mathematics during the 19th and 20th centuries, the number of phenomena labelled “duality” exploded.