From Singularities to Graphs

Abstract

In this text I present some problems which led to the introduction of special kinds of graphs as tools for studying singular points of algebraic surfaces. I explain how such graphs were first described using words, and how several classification problems made it necessary to draw them, leading to the elaboration of a special kind of calculus with graphs. This non-technical paper is intended to be readable both by mathematicians and philosophers or historians of mathematics.

24 pages, 27 figures. A few corrections were performed. Figure 6 is new. Figure 20 is a combination of Figures 19 and 20 of version 1. The paper will appear as a chapter of the volume "When Form Becomes Substance", edited by Luciano Boi and Carlos Lobo (Birkhäuser, 2022)