Who Gave You the Cauchy–Weierstrass Tale? The Dual History of Rigorous Calculus
By Alexandre V. Borovik, Mikhail G. Katz. 2011
70 citations recorded by the source corpus.
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.
Subfields: History and Philosophy of Science, Mathematical Physics, Theoretical Computer Science
View Paper: https://www.semanticscholar.org/paper/7c3d2830da88e1fac109103dbbf2290dcdebf8ab
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Citations in the corpus
- Leibniz's laws of continuity and homogeneity (2012, background): “[3]; Katz and Leichtnam [26]; Katz, Schaps, and Shnider [27].”
- Is mathematical history written by the victors (2013, background): “[14]; Borovik and Katz [16]; Bråting [20]; Katz and Katz [62], [64]; Katz and Tall [69]), have argued that a proto-Weierstrassian view of Cauchy is one-sided and obscures Cauchy’s important contributions, including not only his infinitesimal definition of continuity but also such innovations as his ”
- Ten Misconceptions from the History of Analysis and Their Debunking (2012, background): “Some key developments in this chain are listed in Table 1 (see [19] for more details).”
- Leibniz’s Infinitesimals: Their Fictionality, Their Modern Implementations, and Their Foes from Berkeley to Russell and Beyond (2012, background): “To Cauchy, a sequence “becomes” an infinitesimal if it tends to zero (cf. Borovik & Katz [17]).”