Pierre Samuel et Jules Vuillemin : mathématiques et philosophie

International audienceI examine the relationship between mathematics and philosophy by considering a relatively recent project in philosophy of mathematics: Pierre Samuel's and Jules Vuillemin's reflections and contributions dealing with a general concept of structure in line with Nicolas Bourbaki. I finally study the notion of universal problem.J'examine la relation entre mathématiques et philosophie en considérant un projet relativement récent de philosophie des mathématiques : les contributions et réflexions de Pierre Samuel et Jules Vuillemin portant sur un concept général de structure dans la ligne de Nicolas Bourbaki. J'étudie enfin la notion de problème universel

Euler, Reader of Newton: Mechanics and Algebraic Analysis

International audienceWe follow two of the many paths leading from Newton's to Euler's scientific productions, and give an account of Euler's role in the reception of some of Newton's ideas, as regards two major topics: mechanics and algebraic analysis. Euler contributed to a re-appropriation of Newtonian science, though transforming it in many relevant aspects. We study this re-appropriation with respect to the mentioned topics and show that it is grounded on the development of Newton's conceptions within a new conceptual frame also influenced by Descartes's views sand Leibniz's formalism

Sur une lettre de Descartes à Schooten qu'on dit de 1639

54 pages, version auteurInternational audienceThe aim of this paper is to suggest a new dating for a letter of Descartes to Schooten, stated as probably dating from september 1639 by Adam-Tannery. In this letter, Descartes answers questions dealing with the preparation by Schooten of the 1649 Latin edition of Géométrie, which one concerns his solution of Pappus' problem. I propose to date this letter from march-april 1648 by comparing on the one hand some letters of the Cartesian Correspondence and by using on the other hand a speculative argument based on the study of the controversy between Descartes and Roberval about Pappus' problem.L'objet de cet article est de soumettre une nouvelle datation pour une lettre de Descartes à Schooten, datée possiblement de septembre 1639 par Adam-Tannery. Dans cette lettre, Descartes répond à des questions en relation avec la préparation par Schooten de l'édition latine de la Géométrie de 1649 dont une concerne sa solution du problème de Pappus. Je propose de dater cette lettre de mars avril 1648 en comparant d'une part des lettres de la Correspondance cartésienne et en employant d'autre part un argument spéculatif fondé sur une étude de la controverse entre Roberval et Descartes sur le problème de Pappus

On the alleged simplicity of impure proof

Roughly, a proof of a theorem, is “pure” if it draws only on what is “close” or “intrinsic” to that theorem. Mathematicians employ a variety of terms to identify pure proofs, saying that a pure proof is one that avoids what is “extrinsic,” “extraneous,” “distant,” “remote,” “alien,” or “foreign” to the problem or theorem under investigation. In the background of these attributions is the view that there is a distance measure (or a variety of such measures) between mathematical statements and proofs. Mathematicians have paid little attention to specifying such distance measures precisely because in practice certain methods of proof have seemed self- evidently impure by design: think for instance of analytic geometry and analytic number theory. By contrast, mathematicians have paid considerable attention to whether such impurities are a good thing or to be avoided, and some have claimed that they are valuable because generally impure proofs are simpler than pure proofs. This article is an investigation of this claim, formulated more precisely by proof- theoretic means. After assembling evidence from proof theory that may be thought to support this claim, we will argue that on the contrary this evidence does not support the claim

Pierre Samuel et Jules Vuillemin : mathématiques et philosophie

International audienceI examine the relationship between mathematics and philosophy by considering a relatively recent project in philosophy of mathematics: Pierre Samuel's and Jules Vuillemin's reflections and contributions dealing with a general concept of structure in line with Nicolas Bourbaki. I finally study the notion of universal problem.J'examine la relation entre mathématiques et philosophie en considérant un projet relativement récent de philosophie des mathématiques : les contributions et réflexions de Pierre Samuel et Jules Vuillemin portant sur un concept général de structure dans la ligne de Nicolas Bourbaki. J'étudie enfin la notion de problème universel

(Recension) Luigi Maierù, Le sezione coniche nel Seicento, Soveria Mannelli, Rubbettino Editore, 2009.

Historia Mathematica, Vol. 41, Issue 1, 110-112, 2014

(Recension) « De l’histoire à la philosophie des mathématiques : un programme d’inspiration pragmatiste ? ». Henk J. M. Bos, Redefining Geometrical Exactness : Descartes’ Transformation of the Early Modern Concept of Construction, New York, Springer, 2001.

Les Etudes Philosophiques 2011–2, numéro spécial « Philosophie des Mathématiques », 291-294, 2011

Mathematical notes on Descartes' letters, 1619-1632

In Erik-Jan Bos, Theo Verbeek, and Roger Ariew (éds.), The Correspondence of René Descartes. A New Historico-Critical Edition with Complete English Translation, Oxford, Oxford University Press, vol. I, 1619-1632, forthcoming

(Traduction) Paolo Mancosu, "Philosophie de la pratique mathématique": Ch. VI De l'importance de l'explication mathématique.Ch. VII Au-delà de l'unification.Ch. VIII De la relation entre géométrie plane et géométrie solide.

Paolo Mancosu, Infini, Logique, Géométrie, Paris, Vrin, Partie III, Ch. VI-VIII, p. 275-407

Inventing mathematics in the early modern period. Betwixt tradition and invention

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