Who Gave You the Cauchy–Weierstrass Tale? The Dual History of Rigorous Calculus

Foundations of Science 17 (3):245-276 (2012)
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Abstract

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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Alexandre Borovik
University of Manchester

References found in this work

The Principles of Mathematics.Bertrand Russell - 1903 - Cambridge, England: Allen & Unwin.
Non-standard Analysis.Gert Heinz Müller - 2016 - Princeton University Press.
The Principles of Mathematics.Bertrand Russell - 1903 - Revue de Métaphysique et de Morale 11 (4):11-12.
Proofs and refutations: the logic of mathematical discovery.Imre Lakatos (ed.) - 1976 - New York: Cambridge University Press.

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