Abstract
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.
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Amir Alexander (2014a), "A Brief History of Infinitesimals".
John Allen Paulos (2014), "The 16th Century’s Line of Fire ‘Infinitesimal’".
There are many similar misprints in the book. For example, I am sure Amir Alexander didn't see any of the letters dated 1655 written by Juan Alfonso de Polanco (1517–1576), secretary to Ignatius of Loyola. Because of such obvious errors, I decided not to count them and to look for some general theses.
Amir Alexander (2014b), Infinitesimal.
Robyn Arianrhod (2014), "On a compelling tale of Jesuitsl”.
Judith V. Grabiner (2014), “Review of Amir Alexander, Infinitesimal”.
Amir Alexander, “On Indivisibles and Infinitesimalsl”.
David Sherry, “The Jesuits and the Method of Indivisiblesl”.
Amir Alexander (2014b), "Infinitesimal”, p. 275.
Amir Alexander (2014b), “Infinitesima”, p. 291.
Amir Alexander (2014b), “Infinitesimal”, p. 293.
Pietro Redondi (1988), Galileo Eretico.
Amir Alexander, “On Indivisibles and Infinitesimals”.
Imre Lakatos (1976), “Proofs and Refutations”.
Tiziana Bascelli (2015), “Torricelli's indivisibles”.
Jacqueline A. Stedall (2004) (trans.), The Arithmetic of Infinitesimals.
For example the Online Etymological dictionary gives 1710 as the date for the adjective and 1650s for the noun (https://www.etymonline.com/index.php?allowed_in_frame=0&search=infinitesimal).
J. M. Child (1920), The Early Mathematical Manuscripts of Leibniz.
Gregory of Saint Vincent (2008), Letter 673 in Huygens Œuvres, II, p. 489–490.
Christophorus Clavius S. J. (1603), Romani Calendarii.
References
Alexander, A. (2014). A brief history of infinitesimals: The idea that gave birth to modern calculus. Scientific American. https://www.scientificamerican.com/article/a-brief-history-of-infinitesimals-the-idea-that-gave-birth-to-modern-calculus/.
Alexander, A. (2014). Infinitesimal. How a dangerous mathematical theory shaped the modern world. New York: Scientific American/Farrar, Straus and Giroux.
Arianrhod, R. (2014). On a compelling tale of Jesuits, geometry and heresy in the turbulent 17th century. Times Higher Education, 19 June 2014, https://www.timeshighereducation.com/books/infinitesimal-how-a-da…theory-shaped-the-modern-world-by-amir-alexander/2013940.article.
Alexander, A. On indivisibles and infinitesimals: A response to David Sherry, The Jesuits and the method of indivisibles (to be published).
Bascelli, T. (2015). Torricelli’s indivisibles. In V. Jullien (Ed.), Seventeenth-century indivisibles revisited (p. 115). Berlin: Springer.
Child, J. M. (1920). The early mathematical manuscripts of Leibniz. Chicago: Open Court Publishing.
Clavius, C. S. J (1603). Romani Calendarii a Gregorio XIII p.M. restituti explicatio. Rome.
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. https://www.maa.org/press/maa-reviews/infinitesimal-how-a-dangerous-mathematical-theory-shaped-the-modern-world.
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.
Lakatos, I. (1976). Proofs and refutations. Cambridge: CUP.
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, https://www.nytimes.com/2014/04/08/science/infinitesimal-looks-at-an-historic-math-battle.html?_r=0.
Redondi, P. (1988). Galileo Eretico, Teorino, Enaudi; First English edition: Galileo: Heretic. London: Allen Lane Publishers.
Sherry, D. The Jesuits and the method of indivisibles (to be published).
Stedall, J. A. (2004). (trans.), The arithmetic of infinitesimals. John Wallis 1656. New York: Springer.
Wallis, J. (1655). Arithmetica Infinitorum, Sive Nova Methodus Inquirendi in Curvilineorum Quadraturam, aliaque difficiliora Matheseos Problemata, Oxford. English translation see Stedall.
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Radelet-de Grave, P. Comments on Indivisibles and Infinitesimals: A Response to David Sherry, by Amir Alexander: In View of the Original Book. Found Sci 23, 597–602 (2018). https://doi.org/10.1007/s10699-017-9540-0
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DOI: https://doi.org/10.1007/s10699-017-9540-0