Graphs and lattices in the early versions of Ramon Llull's Art

Abstract

Even though Ramon Llull (c. 1232–1316) made poor use of explicit mathematical formulations, since the times of G.W. Leibniz his Art of finding and demonstrating the truth has been considered an intellectual tool forerunning varied mathematical deployments, from combinatorics, to voting theory and even to computing sciences. This article shows how Llull used implicitly two mathematical formulations, graph theory and lattice theory, not known to have made their appearance before the 20th century: Ars demonstrativa (c.1283) displays some devices of graph theory and Liber principiorum medicinae (c.1274–1283) develops lattice theory in the context of the University of Montpellier.