Cauchy's infinitesimals, his sum theorem, and foundational paradigms
From MaRDI portal
Publication:1616116
DOI10.1007/s10699-017-9534-yzbMath1398.01014arXiv1704.07723OpenAlexW2608300630MaRDI QIDQ1616116
Piotr Błaszczyk, Mikhail G. Katz, Thomas McGaffey, David M. Schaps, Tiziana Bascelli, David Sherry, Kanovei, Vladimir, Alexandre V. Borovik, Karin Usadi Katz, Semen S. Kutateladze
Publication date: 31 October 2018
Published in: Foundations of Science (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1704.07723
History of mathematics in the 19th century (01A55) History of real functions (26-03) One-variable calculus (26A06) Nonstandard analysis (26E35)
Related Items (4)
Fermat's dilemma: Why did he keep mum on infinitesimals? and the European theological context ⋮ Periodic words connected with the tribonacci-Lucas numbers ⋮ Cauchy's work on integral geometry, centers of curvature, and other applications of infinitesimals ⋮ Continuity between Cauchy and Bolzano: issues of antecedents and priority
Cites Work
- Euler's lute and Edwards's oud
- Who gave you the Cauchy-Weierstrass tale? The dual history of rigorous calculus
- Leibniz's infinitesimals: their fictionality, their modern implementations, and their foes from Berkeley to Russell and beyond
- A non-standard analysis of a cultural icon: the case of Paul Halmos
- Eine Erweiterung der Infinitesimalrechnung
- The Olympic medals ranks, lexicographic ordering, and numerical infinities
- Cauchy's Cours d'analyse. An annotated translation
- Infinitely small quantities in Cauchy's textbooks
- Definite values of infinite sums: Aspects of the foundations of infinitesimal analysis around 1820
- Differentials, higher-order differentials and the derivative in the Leibnizian calculus
- Cauchy and the infinitely small
- Hidden lemmas in Euler's summation of the reciprocals of the squares
- Differentials and differential coefficients in the Eulerian foundations of the calculus.
- Cauchy's continuum. A historiographic approach via Cauchy's sum theorem
- Toward a history of mathematics focused on procedures
- Gregory's sixth operation
- Tools, objects, and chimeras: Connes on the role of hyperreals in mathematics
- The Mathematical Intelligencer flunks the Olympics
- Approaches to analysis with infinitesimals following Robinson, Nelson, and others
- Controversies in the foundations of analysis: comments on Schubring's \textit{Conflicts}
- Conflicts between generalization, rigor and intuition. Number concepts underlying the development of analysis in 17th--19th century France and Germany
- Exceptions and counterexamples: understanding Abel's comment on Cauchy's theorem
- Fermat, Leibniz, Euler, and the Gang: The True History of the Concepts of Limit and Shadow
- Sum-avoiding sets in groups
- Commuting and Noncommuting Infinitesimals
- Is mathematical history written by the victors?
- Nonstandard Analysis, Infinitesimals, and the History of Calculus
- Who Gave You the Epsilon? Cauchy and the Origins of Rigorous Calculus
- The Changing Concept of Change: The Derivative from Fermat to Weierstrass
- On Cauchy's Notion of Infinitesimal
- Internal set theory: A new approach to nonstandard analysis
- Higher Trigonometry, Hyperreal Numbers, and Euler's Analysis of Infinities
- Cauchy's Continuum
- Almost Equal: the Method of Adequality from Diophantus to Fermat and Beyond
- Did Weierstrass’s differential calculus have a limit-avoiding character? His definition of a limit inϵ–δstyle
- Geschichte der gleichmäßigen Konvergenz
- Cauchy, Convergence and Continuity
- Rings of Real-Valued Continuous Functions. I
- Non-standard analysis
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
This page was built for publication: Cauchy's infinitesimals, his sum theorem, and foundational paradigms