Sciences, Philosophie, Histoire – UMR 7219, laboratoire SPHERE

Organization : Thomas Berthod, Paul-Emmanuel Timotei et Clément Bonvoisin

PROGRAMME 2023-2024

We will gather on a monthly basis on Fridays in Room Malevitch (483A) building Condorcet, Université Paris-Cité - 4 rue Elsa Morante, 75013 - Paris.
The program will be announced progressively throughout the semester.

Friday, 6th October 2023

Program :

• 2.00 pm - 3.30 pm
  Leo Corry (Tel Aviv University)
  Two Views of Excellence in Research, Two Views of Zionist Nation-Building : Pure Mathematics at the Hebrew University, Applied Mathematics at the Weizmann Institute.
  
  Abstract :
  I will present a comparative analysis of the early years of two world-class centers of mathematical research in Mandatory Palestine, and then in the recently created State of Israel. They pursued different ideals of mathematical excellence which were strongly associated with two different views of Zionism and of the role that science institutions should play in the national project envisioned by each.
  
  The Einstein Institute of Mathematics was established in 1925 at the Hebrew University in Jerusalem (HUJI). Edmond Landau came in 1937 as the first professor and scientific leader, and was succeeded by Avraham Halevy Fraenkel. The neo-humanistic, conceptual spirit of German pure mathematics dominated activities in Jerusalem and it was very much in accordance with a view of Zionism that sought to establish a leading intellectual and spiritual center for the Jewish people in Palestine with a Hebrew University as its flagship.
  
  The Weizmann Institute of Science (WIS) was established about twenty years later in the rural town of Rehovot. It had a thoroughly practical and applied orientation meant to serve the aims of political Zionism in its most activist version, which saw in the creation of a Jewish State in Palestine the most urgent and significant task. A Department of Applied Mathematics was established at WIS in 1948 under the leadership of Chaim Leib Pekeris, whose mathematical views consolidated against the background of his wartime activities at MIT and Columbia, and under the marked influence of John von Neumann. His purpose when joining WIS was to build a high-speed electronic computer and to implement a wide-ranging program of research in various fields of applied mathematics based on computing-intensive methods.
  
  
• 3.30 pm – 4.00 pm
  Break
  
  
• 4.00 pm – 5.30 pm
  Jan von Plato (University of Helsinki)
  New light on Gödel’s life and work
  Abstract :
  Kurt Gödel (1906-1978) was a secretive character who published very little. His foremost result, the incompleteness theorem, revolutionized the foundations of mathematics in 1931. By 1937, he had come half-way through with the solution of Hilbert’s famous first problem about the cardinality of the set of real numbers. After this success, Gödel’s only new published results were about the strange circular-time solutions to the field equations of Einstein’s theory of general relativity he had found in 1949.
  
  The study of Gödel’s tens of thousands of pages of notebooks since 2017, written in an abandoned shorthand, gives a picture of his achievements, as well as of the aims of his life, that is quite different from the one suggested by his publications. As to achievements, there is a plethora of results on logic and foundations of mathematics he revealed to no one. As to the aims, these reflect a vision of science and philosophy he had formed early on in his life, while still a high-school student. Said vision contained that "the world and everything in it has a meaning and makes sense, and it is a good and doubtless meaning.
  So, the talk would be in part about the results Gödel had achieved from 1940 on, when he ceased to publish, in part about his grand program as dictated by his youthful philosophy"

Friday, 17th November 2023

Programme :

• 2 pm - 3.30 pm
  Michael Friedman (The Cohn Institute for the History and Philosophy of Science and Ideas - Humanities Faculty - Tel Aviv University)
  Title : Models and calculations at the end of the 19th century
  Abstract :
  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.
  
  
• 3.30 - 4 pm
  Break
  
  
• 4 pm - 5.30 pm
  Patrick Popescu-Pampu (Laboratoire Paul Painlevé - Université de Lille)
  Title : From infinitely near points to trees and lotuses
  Abstract :
  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.

Friday, 15th December 2023

Homotopy theory

Andrea Gentili (Università di Genova), The homotopical approach to mathematics
Abstract : After introducing with some motivations the homotopical point of view and some of the models for it, I will compare it with the classical one. I will explain how certain classical constructions translate in the homotopical framework and, on the other hand, how some classical categorical constructions can be easily interpreted in the homotopical language.

Jean-Pierre Marquis (Université de Montréal), Why homotopy theory matters to philosophy of mathematics
Abstract : With roots in 19th century mathematics, homotopy theory slowly rose in the 20th century to become a fundamental theory in the 1950s and 1960s. Nowadays, it is central to algebraic topology, its methods are relevant to many other fields and it gave rise to a global foundational framework, namely homotopy type theory. In this talk, I want to focus on the rise of abstract homotopy theory and its significance for philosophy of mathematics.

Practical informations : the session will be held in a hybrid modality. People interested in attending in person are welcome at the Grands Moulins campus of the Université Paris Cité, Bâtiment Condorcet, Salle Malevitch (483A), 4 rue Elsa Morante, 75013 Paris. People interested in attending online may write to bonvoisin.clement@gmail.com with “HPM19-21_15.12.23” as email subject to receive a Zoom link.

Friday, 19th January 2024

Friday, 23rd February 2024

Friday, 22nd March 2024

Friday, 26th April 2024

Friday, 17th May 2024

Friday, 28th June 2024