Foundations of Science

, Volume 23, Issue 4, pp 597–602 | Cite as

Comments on Indivisibles and Infinitesimals: A Response to David Sherry, by Amir Alexander: In View of the Original Book

  • Patricia Radelet-de Grave


A set of six publications have introduced, commented, criticized and defended Amir Alexander’s book on infinitesimals published in 2014. The aim of the following article is to bring the various arguments together.


History of mathematics Indivisibles Infinitesimals Wallis Grégoire de Saint Vincent XVIIth century 


  1. Alexander, A. (2014). A brief history of infinitesimals: The idea that gave birth to modern calculus. Scientific American.
  2. Alexander, A. (2014). Infinitesimal. How a dangerous mathematical theory shaped the modern world. New York: Scientific American/Farrar, Straus and Giroux.Google Scholar
  3. Arianrhod, R. (2014). On a compelling tale of Jesuits, geometry and heresy in the turbulent 17th century. Times Higher Education, 19 June 2014,…theory-shaped-the-modern-world-by-amir-alexander/2013940.article.
  4. Alexander, A. On indivisibles and infinitesimals: A response to David Sherry, The Jesuits and the method of indivisibles (to be published).Google Scholar
  5. Bascelli, T. (2015). Torricelli’s indivisibles. In V. Jullien (Ed.), Seventeenth-century indivisibles revisited (p. 115). Berlin: Springer.Google Scholar
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  8. Grabiner, J. V. (2014). Review of Amir Alexander, infinitesimal: How a dangerous mathematical theory shaped the modern world. Mathematical Association of America, 06/12/2014.
  9. Gregory of Saint Vincent. (2008). In Huygens Œuvres, II, Letter 673, p. 489–490. Quoted in Jean Dhombres et Patricia Radelet-de Grave, Une mécanique donnée à voir, Brepols, Turnhout, Belgium, pp. 104–105.Google Scholar
  10. Lakatos, I. (1976). Proofs and refutations. Cambridge: CUP.CrossRefGoogle Scholar
  11. Paulos, J. A. (2014). The 16th century’s line of fire ‘infinitesimal,’ a look at a 16th-century math battle. The New York Times, April 7, 2014,
  12. Redondi, P. (1988). Galileo Eretico, Teorino, Enaudi; First English edition: Galileo: Heretic. London: Allen Lane Publishers.Google Scholar
  13. Sherry, D. The Jesuits and the method of indivisibles (to be published).Google Scholar
  14. Stedall, J. A. (2004). (trans.), The arithmetic of infinitesimals. John Wallis 1656. New York: Springer.Google Scholar
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Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2017

Authors and Affiliations

  1. 1.Université catholique de LouvainLouvain-la-NeuveBelgium

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