Is mathematical history written by the victors

@article{Bair2013IsMH,
  title={Is mathematical history written by the victors},
  author={Jacques Bair and Piotr Błaszczyk and Robert Erskine Ely and Val{\'e}rie Henry and Vladimir Kanovei and Karin U. Katz and Mikhail G. Katz and S. Kutateladze and Thomas Mcgaffey and David M. Schaps and David Sherry and Steven Shnider},
  journal={Notices of the American Mathematical Society},
  year={2013},
  volume={60},
  pages={886-904}
}
The ABCs of the History of Infinitesimal Mathematics The ABCs of the history of infinitesimal mathematics are in need of clarification. To what extent does the famous dictum “history is always written by the victors” apply to the history of mathematics as well? A convenient starting point is a remark made by Felix Klein in his book Elementary Mathematics from an Advanced Standpoint (Klein [72, p. 214]). Klein wrote that there are not one but two separate tracks for the development of analysis: 

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References

SHOWING 1-10 OF 124 REFERENCES
From the calculus to set theory, 1630-1910 : an introductory history
From the Calculus to Set Theory traces the development of the calculus from the early seventeenth century through its expansion into mathematical analysis to the developments in set theory and theExpand
Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century
TLDR
Mancosu provides the first comprehensive account of the relationship between mathematical advances of the seventeenth century and the philosophy of mathematics of the period with a sophisticated picture of the subtle dependencies between technical development and philosophical reflection. Expand
Who Gave You the Cauchy–Weierstrass Tale? The Dual History of Rigorous Calculus
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 theExpand
Elementary Mathematics from an Advanced Standpoint
THIS book continues the translation of Klein's “Elementar Mathematik” which Messrs. Hedrick and Noble began with their translation of the volume on arithmetic, algebra, and analysis. The volume underExpand
Leibniz on The Elimination of Infinitesimals
My aim in this paper is to consider Leibniz’s response to concerns raised about the foundations of his differential calculus, and specifically with his doctrine that infinitesimals are “fictions,”Expand
A short life of Euler
This article offers an overview of the life and work of Leonhard Euler (1707–83). During 2007 Euler's tercentenary was celebrated by mathematicians around the world. The Open University Centre forExpand
Infinitesimals as an Issue of Neo-Kantian Philosophy of Science
  • T. Mormann, M. Katz
  • Mathematics, Physics
  • HOPOS: The Journal of the International Society for the History of Philosophy of Science
  • 2013
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Differentials and differential coefficients in the Eulerian foundations of the calculus
Abstract In the 18th-century calculus the classical notion of quantity was understood as general quantity, which was expressed analytically and was subject to formal manipulation. Number wasExpand
God Created the Integers: The Mathematical Breakthroughs That Changed History
"God Created The Integers" is Stephen Hawking's personal choice of the greatest mathematical works in history. He allows the reader to peer into the mind of genius by providing us with excerpts fromExpand
Mathematics as a Numerical Language
TLDR
This chapter discusses the role of mathematics as a numerical language, and provides examples from probability theory, from algebra, and from elementary algebraic topology. Expand
...
1
2
3
4
5
...