Ten Misconceptions from the History of Analysis and Their Debunking

TL;DR

This paper debunks common misconceptions about the history of analysis, especially the false idea that infinitesimals were eliminated by the early 20th-century founders, highlighting ongoing work on infinitesimal-enriched systems.

Contribution

It challenges the dominant historical narrative by showing that infinitesimals persisted and were actively developed beyond the so-called 'great triumvirate' of analysis.

Findings

Infinitesimals were not eliminated but continued to be developed.

Historical distortions arise from a narrow view of the continuum.

The received history oversimplifies the evolution of analysis.

Abstract

The widespread idea that infinitesimals were "eliminated" by the "great triumvirate" of Cantor, Dedekind, and Weierstrass is refuted by an uninterrupted chain of work on infinitesimal-enriched number systems. The elimination claim is an oversimplification created by triumvirate followers, who tend to view the history of analysis as a pre-ordained march toward the radiant future of Weierstrassian epsilontics. In the present text, we document distortions of the history of analysis stemming from the triumvirate ideology of ontological minimalism, which identified the continuum with a single number system. Such anachronistic distortions characterize the received interpretation of Stevin, Leibniz, d'Alembert, Cauchy, and others.