Séminaire – Mathématiques 19e-21e, histoire et philosophie

Programme :

• 14h-15h30
  Michael Friedman (The Cohn Institute for the History and Philosophy of Science and Ideas – Humanities Faculty – Tel Aviv University)
  Titre : Models and calculations at the end of the 19th century
  Résumé :
  On November 7th, 1886 Alexander Brill gave a lecture on the collection of material mathematical models at the university of Tübingen. These models usually modelled various algebraic surfaces and curves of various degrees, and were wide spread in Germany during the last third of the 19 th century. In this lecture, after describing the preparation of models from various materials (plaster, strings, cardboard) usually by students, he notes that these students could “write a paper on this [subject], the publication of which […] played no small part in encouraging one to carry out the often-arduous calculations […],” implicitly noting that calculations precede the formulation and the proving of theorems. Brill then continues, claiming that the reverse direction also occurred : “the model often prompted subsequent investigations into the specific features of the represented structure.” [Alexander Brill, “Über die Modellsammlung des mathematischen Seminars der Universität Tübingen (Vortrag vom 7. November 1886),” Mathematisch naturwissenschaftliche Mitteilungen 2 (1887), 69–80.] Thus, according to Brill, mathematical models did not merely serve to visualize lengthy calculations, they were also an object of research, and prompted not only the discovery of new theorems but also ways to prove them.
  My talk will ask whether this statement was only a rhetorical one, meant to further support such model collection (and perhaps others collections), or whether indeed Brill or other mathematicians considered calculations, modeling and proving mathematical claims as supporting and essential to each other. I will also attempt to characterize the changing role of calculation, when the tradition of material models declined and when the term “model” acquired new meaning during the 1920s and the 1930s, signifying procedures of abstraction and mathematical representation of certain well-selected processes.
• 15h30-16h
  Pause
• 16h-17h30
  Patrick Popescu-Pampu (Laboratoire Paul Painlevé – Université de Lille)
  Titre : From infinitely near points to trees and lotuses
  Résumé :
  I will explain what are the constellations of infinitely near points, how they were codified by various kinds of trees, and how these trees may be compared by embedding them in lotuses.

Lieu : Salle Malevitch (483A) bâtiment Condorcet