Article ID: CBB001252708

Who Gave You the Cauchy-Weierstrass Tale? The Dual History of Rigorous Calculus (2012)


Cauchy's contribution to the foundations of analysis is often viewed through the lens of developments that occurred some decades later, namely the formalisation of analysis on the basis of the epsilon-delta doctrine in the context of an Archimedean continuum. What does one see if one refrains from viewing Cauchy as if he had read Weierstrass already? One sees, with Felix Klein, a parallel thread for the development of analysis, in the context of an infinitesimal-enriched continuum. One sees, with Emile Borel, the seeds of the theory of rates of growth of functions as developed by Paul du Bois-Reymond. One sees, with E. G. Björling, an infinitesimal definition of the criterion of uniform convergence. Cauchy's foundational stance is hereby reconsidered.

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Authors & Contributors
Cauchy, Augustin Louis
Schubring, Gert
Katz, Mikhail G.
Fischer, Gordon
Belhoste, Bruno
Gilain, Christian
Archive for History of Exact Sciences
Archives Internationales d'Histoire des Sciences
Foundations of Science
Sciences et Techniques en Perspective
Bulletin de la Société des Amis de la Bibliothèque de l'École Polytechnique
NTM: Zeitschrift für Geschichte der Naturwissenschaften, Technik und Medizin
Mathematical analysis
Number theory; number concept
Cauchy, Augustin Louis
Weierstrass, Karl Theodor
Cantor, Georg Ferdinand Ludwig
Lagrange, Joseph Louis
Du Bois-Reymond, Paul
Lewis, W. David
Time Periods
19th century
20th century, early
18th century
École Polytechnique, Paris

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