Article ID: CBB001252715

Ten Misconceptions from the History of Analysis and Their Debunking (2013)

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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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Authors & Contributors
Ferreirós, José
Katz, Mikhail G.
Dujac, Pierre
Gardies, Jean-Louis
Grattan-Guinness, Ivor
Moore, Matthew E.
Journals
Historia Mathematica
Synthese
Bollettino di Storia delle Scienze Matematiche
Revue Philosophique de la France et de l' Étranger
Science in Context
Perspectives on Science
Publishers
Princeton University Press
Crítica
Indiana University
Concepts
Mathematics
Mathematical analysis
Infinitesimals
Set theory
Calculus
Logic
People
Dedekind, Richard
Cantor, Georg Ferdinand Ludwig
Weierstrass, Karl Theodor
Cohen, Hermann
Cassirer, Ernst
Hilbert, David
Time Periods
19th century
20th century, early
20th century, late
17th century
Places
Germany
France
China
Europe
Italy
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