Who Gave you the Cauchy-Weierstrass Tale? The Dual History of Rigorous Calculus

Details Who Gave you the Cauchy-Weierstrass Tale? The Dual History of Rigorous Calculus Who Gave you the Cauchy-Weierstrass Tale? The Dual History of Rigorous Calculus

2011-08-14

arxiv.org/abs/1108.2885v2

Mathematics

History and Overview

46 pages, 3 figures; Foundations of Science, 2011, http://www.springerlink.com/content/p245331307229823/

Scientific paper

10.1007/s10699-011-9235-x

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. Bjorling, an infinitesimal definition of the criterion of uniform convergence. Cauchy's foundational stance is hereby reconsidered.

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