Of pashas, popes, and indivisibles

TL;DR

This paper explores the historical and theological context of Cavalieri's indivisibles, analyzing sources from the 17th to 21st centuries to understand their broader implications.

Contribution

It investigates the religious and geopolitical factors influencing the debate over indivisibles and Cavalieri's mathematical work, linking historical context to mathematical critique.

Findings

Historical roots of the indivisibles debate are deeply intertwined with theological issues.

The suppression of Cavalieri's religious order is connected to the controversy over his mathematical methods.

The study offers a comprehensive analysis of sources spanning four centuries.

Abstract

The studies of Bonaventura Cavalieri's indivisibles by Giusti, Andersen, Mancosu and others provide a comprehensive picture of Cavalieri's mathematics, as well as of the mathematical objections to it as formulated by Paul Guldin and other critics. An issue that has been studied in less detail concerns the theological underpinnings of the contemporary debate over indivisibles, its historical roots, the geopolitical situation at the time, and its relation to the ultimate suppression of Cavalieri's religious order. We analyze sources from the 17th through 21st centuries to investigate such a relation.