Article ID: CBB925230600

Continuity Between Cauchy and Bolzano: Issues of Antecedents and Priority (2020)


In a paper published in 1970, Grattan-Guinness argued that Cauchy, in his 1821 Cours d'Analyse, may have plagiarized Bolzano's Rein analytischer Beweis (RB), first published in 1817. That paper was subsequently discredited in several works, but some of its assumptions still prevail today. In particular, it is usually considered that Cauchy did not develop his notion of the continuity of a function before Bolzano developed his in RB and that both notions are essentially the same. We argue that both assumptions are incorrect, and that it is implausible that Cauchy's initial insight into that notion, which eventually evolved to an approach using infinitesimals, could have been borrowed from Bolzano's work. Furthermore, we account for Bolzano's interest in that notion and focus on his discussion of a definition by Kästner (in Section 183 of his 1766 book), which the former seems to have misrepresented at least partially.

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Authors & Contributors
Cauchy, Augustin Louis
Guillén, Elías Fuentes
Grabiner, Judith V.
Spalt, Detlef D.
Moore, Matthew E.
Meo, M.
Historia Mathematica
Archive for History of Exact Sciences
Archives Internationales d'Histoire des Sciences
History and Philosophy of Logic
Foundations of Science
Sociedad Andaluza de Educación Matemática THALES
Harvard University Press
Indiana University
Publicaciones de la Universidad de Alicante
Mathematical analysis
Functions (mathematics)
Cauchy, Augustin Louis
Bolzano, Bernard
Cantor, Georg Ferdinand Ludwig
Dedekind, Richard
Bjorling, Emmanuel Gabriel
Kronecker, Leopold
Time Periods
19th century
20th century
18th century
20th century, early
École Polytechnique, Paris
University of Prague

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