Sciences, Philosophie, Histoire – UMR 7219, laboratoire SPHERE

Le séminaire d’histoire et de philosophie des mathématiques modernes est un lieu de présentation et de discussion de textes mathématiques produits aux 19e, 20e et 21e siècles, dans des perspectives aussi bien historiques que philosophiques. Il entend servir de lieu d’exploration (lecture, traduction, explication) de documents mathématiques peu ou mal connus, mais également de présentation de travaux en cours sur ces périodes. L’accent est mis sur la proximité avec les sources textuelles. Les séances prennent, le plus souvent, la forme d’une discussion desdites sources (auxquelles les orateurs donnent accès au préalable), précédée d’un exposé historique ou mathématique.

Organisation : Thomas Berthod, Clément Bonvoisin, Karine Chemla, Sara Confalonieri, Frédéric Jaëck (AMU, & SPHere), Nicolas Michel (Bergische Universität Wuppertal, Fakultät für Mathematik und Naturwissenschaften, & SPHere), Ivahn Smadja (Université de Nantes, & SPHere), Paul-Emmanuel Timotei

Contact : F. Jaëck

RÉSUMÉS

Mardi 17 janvier, 14:00 - 16:00, salle Rothko, 412B, hybride

• Claudio Bartocci (DIMA, Università di Genova) et Jean-Jacques Szczeciniarz (Université Paris Cité, HPS, SPHere)
  L’existence de l’inexistant, une nouvelle problématique, celle du corps à un élément
  Trois points seront abordés :
  1. Histoire et présentation du problème depuis l’apparition de FUN dans le travail de Jacques Tits (1958) en passant par les résultats de quelques mathématiciens, Manin, Kapranov, Soulé, Deitmar.
  2. Une nouvelle présentation à travers les travaux (résumés) de Toën Vaquié, et notre compréhension (CB AG JJS) du problème. Ce qu’apporte le point de vue catégoriel.
  3. Philosophie des mathématiques, comment inexister ? Rapide comparaison avec racine de moins 1. La puissance synthétique de la distorsion des objets.

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Mardi 14 février, 9:30 - 12:30, salle Rothko, 412B, hybride

• Peter Ullrich (Universität Koblenz-Landau)
  The theory of analytic factorials - a quarrel between proofs and computations
  Already at the beginning of the 19th century it was known that the factorial can be interpolated as an analytical function, at least on the positive real numbers, by means of the Gamma integral. However, some mathematicians tried to end interpolations in other ways, by setting up functional equations that these analytic factorials should satisfy and then trying to compute analytic expressions for them.
  A. L. Crelle, for example, published a whole book on the subject in 1823, which led to a sharp response from M. Ohm in 1829. K. Weierstraÿ brought clarification here, who clearly recognized that the interpolation problem has no unique solution and was thus able to correct Crelle and refute Ohm. Regarding the publication of his results, Weierstraÿ declined Crelle's o er of the Journal für die reine und angewandte Mathematik for this purpose, choosing instead his school’s 1843 program. It was not until 1856 that he published an expanded version in Crelle’s Journal.

• Valeriya Chasova (PLUS, GW Fakultät, Fachbereich Philosophie ; Archives Henri-Poincaré, UniStra/ULorraine/CNRS ; CEFISES, UCLouvain)
  Physical significance versus mathematical surplus in philosophy and history
  Not all there is in physical theory has physical significance (in the sense of contributing to predictions or to ontology of the physical world). There are also elements coming from mathematics and usually interpreted as idle. Separating this mathematical surplus from physical content is an important and non-trivial task. I will tell more (where possible in simple terms) about ways to accomplish it and related topics in recent philosophy and in XX century history.
  A still common solution in philosophy of physics, going back to Leibniz in his debate with Clarke (1717), is to count as mathematical surplus what varies under theoretical symmetry transformations. However, it has been defended from Kosso (2000) on that symmetry-variant elements have physical significance provided the theoretical symmetries concerned are matched with symmetries in the world or with conservation laws.
  Historically, Klein (1917) argued that energy-momentum conservation law is unphysical in Einstein’s just formulated general relativity (1915) because of not being linked appropriately with the field equations. However, Hilbert (Klein, 1917) took this to be a hallmark of that theory, while Noether (1918) showed that this feature is characteristic of a class of theories with certain symmetries. But her solution was itself mathematical, and its physical import only got better clarified later on.
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Lundi 6 mars, !! 13:30 - 16:30, salle Gris, 734A !!, hybride

• Walter Dean
  On models and computation in geometric consistency proofs
  The focus of the talk will be a method for transforming several of Hilbert’s (1899) model-theoretic consistency proofs for Euclidean and non-Euclidean geometries into syntactic demonstrations originally exposited by Paul Bernays (1935, 1939). Bernays’ method is of historical interest due its apparent relation to the Frege-Hilbert controversy. But it is also of mathematical interest because of the specific combination of proof-theoretic, analytic, and algorithmic techniques which it employs. Time permitting, I will also discuss how this method anticipates contemporary developments in reverse mathematics and automated theorem proving.

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Mardi 18 avril, 13:30 - 16:30, salle Rothko, 412B, hybride

• Karine Chemla (CNRS, SPHere)
  From computation to a practice of proof through the introduction of a concept : Poncelet’s ideal elements in geometry
  In a first part of this presentation, I intend to return to the nature of the “ideal elements” that Jean-Victor Poncelet introduced into geometry, notably in his Traité des Propriétés Projectives des Figures (1822). This analysis will require that I discuss some features of the diagrams used by Poncelet. Moreover, I will examine the use of elements of this kind in the practice of proof to which the Traité des Propriétés Projectives des Figures attests. In a second part, I will turn to the notebooks that Poncelet wrote in Saratov, as a prisoner of war, between March 1813 and June 1814, to shed light on the part played by Poncelet’s analytical approaches at the time in the genesis of the concept of ideal elements. This talk is based on joint work with Bruno Belhoste.

• Clément Bonvoisin (Université Paris Cité, ED 623, SPHere)
  From Schwarz-Weiß-Steuereungen to bang-bang controls. Mathematical translations of an engineering problem in the dissertation of Donald Bushaw(1952)
  In May 1952, Donald Bushaw (1926 – 2012) defended his Ph.D. thesis, titled “Differential equations with a discontinuous forcing term,” at Princeton University. In their report, the examiners wrote that the dissertation engaged a previously unexplored question (the study of what Bushaw called bang-bang controls), using novel methods. However, the problem Bushaw tackled in his thesis was inspired by research carried during World War II by a team of German engineers, who worked on what they called Schwarz-Weiß-Steuerungen (black-white controls). Bushaw acknowledged this inspiration by commenting the work of one of these engineers, Irmgard Flügge-Lotz (1903 – 1974), who moved from Europe to Stanford in 1948. What I wish to explore in this talk is the way Bushaw built his work on that of Flügge-Lotz and her coworkers : how did he get to know of the German works ? How did he translate an engineering problem into a mathematical one ? And, in the process, how did he reshape the problem, what did he emphasise on, what did he discard ?

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Mardi 16 mai, 9:30 - 12:30, salle Rothko, 412B - Université Paris Cité, bâtiment Condorcet. 4, rue Elsa Morante, 75013 - Paris

• Patrick Popescu-Pampu, Université de Lille et Laboratoire Paul Painlevé
  Que signifie résoudre les singularités d’une courbe algébrique plane ?
  J’examinerai plusieurs sens de la notion de résolution des singularités des courbes algébriques planes, ainsi que plusieurs méthodes de résolution.
  
• Paul-Emmanuel Timotei, Université Paris Cité et Laboratoire SPHERE
  La réduction des singularités d’une courbe algébrique plane par correspondance chez Georges-Henri Halphen.
  Je présenterai une technique de réduction des singularités des courbes algébriques planes se trouvant dans l’appendice du Traité de géométrie analytique (courbes planes) de George Salmon (édition française de 1884) : « Etude sur les points singuliers des courbes algébriques planes » de Georges-Henri Halphen.
  
  
  Télécharger le programme
  
  

  

  
  

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Vendredi 2 juin, 14:00 - 17:00, salle Rothko, 412B, hybride

• Klaus Volkert Wuppertal/Luxemburg
  The early history of duality
  In my talk I will study three strands of the early history of duality : the theory of ploygons and polyhedra, the case of spherical geometry and the classic polar reciprocity. We will look for the base and the function of duality particular to the different fields, and we will analyze its common features. What is duality, why is there duality, and why it is so useful ?
  
  Lit. Etwein, F./Voelke, J.-D./Volkert, K. : Dualität als Archetypus mathematischen Denkens (Göttingen : Cuvillier, 2019).

• Tinne Hoff Kjeldsen (University of Copenhagen )
  From Mathematical Programming to Convex Analysis : Duality as a driving force in history of mathematics
  The presentation will focus on the emergence of convex analysis in the 20th century in the context of mathematical programming with special attention to the significance of duality. More specific, we will look at duality in the history of mathematical programming from von Neumann’s work in game theory to Fenchel’s duality theorem in nonlinear programming and the role it played for the development of convex analysis. How did ideas of duality emerge in linear programming ? What role did they play for the development of nonlinear programming ? How did Fenchel introduce ideas of duality in nonlinear programming and how did his duality function as a driving force for the development of convex analysis ?