Galois Connections: Mathematics, Art, and Archives

Abstract

Évariste Galois (1811–1832) has been increasingly recognised as an important mathematician who despite his short life developed mathematical ideas that today have led to applications in computer science (such as Galois connections) and elsewhere. Some of Galois’ mathematics can be visualised in interesting and even artistic ways, aided using software. In addition, a significant corpus of the historical documentation on Galois and his family (including his brother Alfred Galois, who was an artist), can now be accessed online as a growing number of institutional archives digitise their collections. This paper introduces some of the mathematics of Galois, ways in which it can be visualised, and also considers the issues and new opportunities with respect to visualising information on Galois and his family (including the connections between them). Although the story of Galois and his close relations can be seen as one of tragedy with lives cut short, from a historical viewpoint Évariste Galois’ contribution to humankind has been a triumph.