Computers in mathematical practice: an exercise of micro history

Abstract

The use of computers in mathematical practices is a theme for philosophical, historical and sociological reflections. Samples of the myriad of questions that arise when mathematics definitively incorporates computers in its domain can be drawn from the analysis of the peculiar case of the proof of the Four Colour Theorem. Invariably the usual accounts of the philosophical relevance of this celebrated mathematical result are rooted in the questions raised from Thomas Tymoczko's introduction to experimentation in mathematics. The purpose of this paper is to present an alternative detailed narrative, a kind of microhistory exercise, as a background for the mapping of some philosophically relevant questions that can still be instigated by the case of the Four Colour Theorem. We intend to maintain that the relevance of this case is not reduced to that of serving as an illustration of a historical or sociological curiosity in mathematics or computer science, but may still be a source of interesting conceptual problems for the philosophy of mathematical practice, in the interface with the philosophy of computer science.