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Accueil > Archives > Séminaires des années précédentes > Séminaires 2014–2015 : archives > Mathematics and Philosophy, 19th and 20eth Centuries 2014–2015

Axis History and philosophy of mathematics

Mathematics and Philosophy, 19th and 20eth Centuries 2014–2015

Organisers : Sylvain Cabanacq,
Emmylou Haffner,
David Rabouin

This working group aims to build an informal space for PhD students working on 19th and 20th Century, whether they are historians or philosophers, to discuss and work together as well as with researchers, students in mathematics and master students.

No prerequisites are expected from participants. On the contrary, the idea is to share historical knowledge, mathematical skills, philosophical insights and points of view. Our starting points will go from recent papers, discussed together, to mathematical theories (for example, group representation) or more “classical” historical and philosophical writings (Weyl, Lautman, …). This year, the group will be organized in series of sessions united by a theme. A large part of each session will be devoted to questions and discussion.

Current year
Archives : 2015-2016, 2013-2014, 2012-2013, 2011-2012.

PROGRAMME 2014–2015 :
twice a month, Thursdays, 10:00–13:00, Room Rothko, 412B, University Paris Diderot, Building Condorcet, 75013 Paris – Access map.

Gödel and Philosophy (three sessions)

October 16

Mark van Atten (IHPST)
A failing project : on Gödel’s reception of Leibniz, Husserl and Brouwer

October 30

Juan-Luis Gastaldi (SPH, Univ. Montaigne, Bordeaux)
Arithmétique et contenu dans le processus de mathématisation de la logique au XIXe siècle.

November 13

Gabriella Crocco (CEPERC, Univ. Aix-Marseille)
Autour de manuscrits inédits.

December 12
Around Moritz Pasch (two sessions)
Dirk Schlimm (MacGill University)
Pasch’s empiricist philosophy of mathematics.

Tuesday January 27
, 10:00 – 13:00

Session prepared by Samson Duran (GHDSO, Paris-Sud) and Simon Decaens (Univ. Paris Diderot, SPHERE)
Sur les méthodes quantitatives en histoire des mathématiques.
A free discussion with Laurent Rollet (Archives Poincaré, Université de Lorraine) will succeed, on the works of the PhDs Students, and their interrogations.

Tuesday February 10
, 9:30 – 12:30

Sylvain Cabanacq (Univ. Paris Diderot, SPHERE)
Introduction aux structures o-minimales : quelques résultats fondamentaux.
Introduites au début des années 1980 en théorie des modèles, les structures o-minimales ont rapidement été considérées comme une généralisation adéquate des géométries semi-algébrique et sous-analytique. Articulant des propriétés comme l’élimination des quantificateurs ou la model-complétude à des résultats de nature topologique, comme la décomposition cellulaire, ces structures établissent un lien entre logique et géométrie, dont les applications se révèlent nombreuses. Nous souhaiterions dans cet exposé présenter les notions essentielles dans ce cadre et certains des résultats fondamentaux.

Tuesday March 3
, 9:30 – 12:30

Maarten Bullynck (Univ. Paris 8 & SPHERE)
A la recherche de l’essence des démonstrations mathématiques allemandes au début du XIXe siècle.

Tuesday March 24
, 9:30 – 12:30

David Rowe (Gutenberg Univ., Mayence)
On visualizing quartic surfaces in the 1860s.
The decade of the 1860s saw an explosion of interest in the theory of quartic surfaces, particularly in the wake of Kummer’s studies of ray systems in geometrical optics. Plücker classified special types of quartics as a way of visualizing caustic surfaces formed by congruences of lines in quadratic line complexes. These Plücker surfaces were envelopes of lines, whereas Darboux studied the special quartics known as generalized cyclides that arise as envelopes in sphere geometry. The connection between Kummer surfaces and generalized cyclides was discovered by Lie when he and Klein visited Paris in 1870. This led to their joint paper on the asymptotic curves on Kummer surfaces. These examples, along with numerous others, mark the 1860s as a true era of discovery for classical algebraic geometry.

Tuesday March 31
, 9:30 – 12:30

David Rowe (Gutenberg Univ., Mayence)
On the early works of Klein and Lie, 1869-1872.
The brief collaboration between Klein and Lie during these early years contains the germinating ideas for many of their later works. Both took inspiration from the works of Plücker, Clebsch, and Darboux in ways that have been little noticed before. Lie was by far the more creative thinker, but he had great difficulty working out his ideas in a comprehensible form. Klein thus wrote up some of Lie’s early papers, and in a few cases they published together, which was quite rare in those days. Drawing on Klein’s letters to Lie, I will attempt to clarify the nature of their relationship and gauge the importance of this early work for their subsequent research.

Tuesday April 7
, !!! 9:30 – 12:30 !!!, room Rothko, 412B
Working Group : exact sciences : 1/2
2 joint sessions with PHD Students : Working group in History and philosophy of physics

José Ferreiros (Univ. of Sevilla)
Unreasonable Effectiveness in Context : some historical remarks on Wigner’s famous 1960 paper.

 !! Tuesday April 14
, 14:00 — 17:00 !!, joint session with the seminar History and Philosophy of Mathematics
, 14:00 – 17:00

David Rowe (Gutenberg Univ., Mayence)
On editing Mathematische Annalen, 1872-1928.
The founding of Mathematische Annalen by Alfred Clebsch (Göttingen) and Carl Neumann (Leipzig) created an important forum for mathematicians in Germany who stood outside the dominant centre in Berlin. Beginning in 1876, Felix Klein and Adolf Mayer served as its principal editors, complemented by Walther von Dyck in 1888. Later, in 1901, David Hilbert joined the Hauptredaktion, supported by Otto Blumenthal from 1905 onward. During these different periods, editorial policies differed greatly, though the Annalen had already by 1880 emerged as one of the leading journals under Klein’s guidance. Both Klein and Hilbert took a strong international orientation, a stance that was gradually undermined by the political activities of L.E.J. Brouwer, who joined the editorial board during the early war years. After describing various aspects of the editorial work behind the scenes, I will take up the tumultuous events of the 1920s that ultimately led to Brouwer’s ouster from the editorial board. My analysis suggests that Hilbert’s motivation for this action had little to do with the famous foundations debate that pitted Hilbert’s formalism against Brouwer’s intuitionism but rather that Hilbert felt compelled to act in order to counteract his rival’s political influence on the future direction of the journal.

 !! Tuesday May 5 !! Afternoon, Room Rothko, 412B !!
, 13:30 – 16:30

Autour de Moritz Pasch (2/2)
Philippe Nabonnand (Archives Poincaré, Univ. de Lorraine)
Moritz Pasch, un empiriste chez les mathématiciens.

Thursday May 28, 10:00 – 13:00, !! Room Kandinsky, 631 B !!
Working Group : exact sciences : 2/2
2 joint sessions with PHD Students : Working group in History and philosophy of physics

Frédéric Brechenmacher (Ecole polytechnique)
Les Méthodes nouvelles de la mécanique céleste d’Henri Poincaré, témoin des interactions entre mécanique et algèbre au XIXe siècle.
L’approche de Poincaré sur le problème des trois corps a souvent été célébrée comme un point d’origine de l’étude des systèmes dynamiques et de la théorie du chaos. Cet exposé propose de porter un autre regard sur cette approche en analysant le rôle crucial qu’y joue une forme traditionnelle d’interface entre mécanique et algèbre par l’intermédiaire d’une équation particulière - l’ « équation à l’aide de laquelle on détermine les inégalités séculaires des planètes » -qui dévoile une culture mathématique spécifique au XIXe siècle.

Thursday June 23
, 9:30 - 12:30, Room Rothko, 412B

  • Martin Hils (Univ. Paris Diderot, Equipe de Logique)
    Pila-Wilkie theorem and diophantine geometry.