Ten Misconceptions from the History of Analysis and Their Debunking

By Piotr Błaszczyk, Mikhail G. Katz, David Sherry. 2012

49 citations recorded by the source corpus.

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.

Subfields: History and Philosophy of Science, Mathematical Physics, Theoretical Computer Science

View Paper: https://www.semanticscholar.org/paper/96380791419776556fee2d6aab11a06e2c968228

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In History and Philosophy of Science

1. David Sherry
2. Mikhail G. Katz
3. Piotr Błaszczyk
4. J. McGrane

In Mathematical Physics

1. Mikhail G. Katz
2. David Sherry
3. Piotr Błaszczyk

In Theoretical Computer Science

1. Mikhail G. Katz
2. David Sherry
3. Piotr Błaszczyk
4. R. Ely

Citations in the corpus

• Is mathematical history written by the victors (2013, background): “[14]; Borovik & Katz [16]; Br̊ating [20]; Katz & Katz [65], [67]; Katz & Tall [72]), have argued that a proto-Weierstrassian view of Cauchy is onesided and obscures Cauchy’s important contributions, including not only his infinitesimal definition of continuity but also such innovations as his infini”
• Leibniz’s Infinitesimals: Their Fictionality, Their Modern Implementations, and Their Foes from Berkeley to Russell and Beyond (2012, methodology): “imal expansion of the root of any polynomial, the same algorithm we find later in Cauchy’s proof of the intermediate value theorem” [43, p. 733]. The matter is discussed in detail in Bla szczyk et al. [15]. See also footnote 62. LEIBNIZ’S INFINITESIMALS 49 sequence b n of successive approximations, a”
• Leibniz's laws of continuity and homogeneity (2012, background): “Stevin initiated a systematic approach to decimal representation of measuring numbers, marking a transition from a discrete arithmetic as practiced by the Greeks, to the arithmetic of the continuum taken for granted today (see [41], [44], and [2]).”