Ten Misconceptions from the History of Analysis and Their Debunking

Details Ten Misconceptions from the History of Analysis and Their Debunking Ten Misconceptions from the History of Analysis and Their Debunking

2012-02-19

arxiv.org/abs/1202.4153v1

Mathematics

History and Overview

46 pages, 4 figures; Foundations of Science (2012). arXiv admin note: text overlap with arXiv:1108.2885 and arXiv:1110.5456

Scientific paper

10.1007/s10699-012-9285-8

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.

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