logo Sphere
Logo Université Paris-Diderot Logo Université Paris1-Panthéon-Sorbonne


On this website

On the whole CNRS Web

Home > Archives > Previous years: Seminars > Seminars 2020-2021: archives > Mathematics 19th – 21st, History and Philosophy 2020–2021

Axis History & philosophy of mathematics

Mathematics 19th – 21st, History and Philosophy 2020–2021

The Seminar Mathematics 19th – 21st, History and Philosophy is a place for the presentation and discussion of mathematical texts produced in this period, from both historical and philosophical perspectives. It intends to serve as a place of exploration (reading, translation, explanation) of little or poorly known mathematical documents, but also of presentation of work in progress during these periods. The emphasis is on proximity to textual sources. The sessions most often take the form of a discussion of said sources (to which the speakers give prior access), preceded by a historical or mathematical presentation.

Organisation: Frederic Jaeck (ENS), Nicolas Michel (Utrecht University, Dpt of Mathematics, & SPHere)

To current year and archives 2011–

PROGRAM 2020-2021
We will meet by webconference, once a month, from 4pm to 6pm.
Working languages will be French and English.

Mo 12/7/2020 Tu 01/12/2021 Fr 02/5 Tu 03/16 Fr 04/16 Tu 05/18 Fr 06/11
To participate, texts and link Zoom, please write latest eve of the session to the organisers: N. Michel or F. Jaëck

Monday 12/7/2020, 4pm to 6pm, webonference
  • David Waszek (McGill University)
    ‘Calculus’ as Method or ‘Calculus’ as Rules? Boole against Frege on a systematic method for logic
    • Document: reading of extracts 1 & 2 recommended
      French translations are also available at the following references:
      . G. Boole, Les lois de la pensée, trad. Souleymane Bachir Diagne, 1992, Vrin
      . G. Frege, Écrits posthumes, ss. dir. Ph. de Rouilhan et Cl. Tiercelin, 1999, Nîmes, éd. Jacqueline Chambon

Tuesday 01/12/2021, 4pm to 6pm, webconference

  • Discussion on the translation of the Bericht of Brill & Noether

Friday 02/5/2021, 4pm to 6pm, webconference

  • Bruno Belhoste (Université Paris 1)
    Entre analyse et géométrie, l’approche de Monge
    We will examine how Monge considered the relationship between geometric constructions and algebraic calculus in his research and his teaching. For this, we will use a few examples taken from his courses at the École normale in year III and at the École polytechnique.

Tuesday March 16, 4pm to 6pm, webconference

  • Dirk Schlimm (McGill University)
    Discussion on Boole & Frege on the aims of a logical calculus (follow session of Dec. 7)

Friday April 16, !! 3pm !!–6pm, webconference

  • Christopher Hollings (Oxford University)
    Meeting under the integral sign? The Oslo Congress of Mathematicians on the eve of the Second World War
    Oral communication, and congresses in particular, remain a crucial element within mathematical communication – even in the current age of electronic mail. Indeed, congresses and meetings serve many more purposes than simply communicating information about recent mathematical research, and this has always been the case, with each particular historical period setting different priorities. The present talk is drawn from a book, recently completed with Reinhard Siegmund-Schultze, which focuses upon and stresses the historically unique character of the Oslo International Congress of Mathematicians of 1936. This congress was the only one on this level to be held during the period of the Nazi regime in Germany (1933–1945) and after the wave of emigrations from it. In this talk, I will survey the differences between the goals of the various participants in the congress, most particularly the Norwegian organisers, and the Nazi-led German delegation. I will consider also the background to the absence of the proposed Soviet and Italian delegations. If time permits, I will also go into the mathematical dimension of the Oslo congress, this being the conference at which the Fields Medals were awarded for the first time. Overall, the Oslo congress may be used as a lens through which to view the state of the art of mathematics in the mid-1930s.

Tuesday May 18, 4pm to 6pm, webconference

  • Nicolas Michel (Utrecht University, Dpt of Mathematics, & SPHere)
    Intuition, calcul, et raisonnement. Philosophie et pratique de la géométrie chez Hieronymous Zeuthen

Firday June 11, 4pm to 6pm, webconference

  • Jamie Tappenden (Université du Michigan)
    Frege, Carl Snell and Romanticism; Fruitful Concepts and the Organic/Mechanical Distinction
    A surprisingly neglected figure in Frege scholarship is the man Frege describes (with praise that is very rare for Frege) as his "revered teacher", the Jena physics and mathematics professor Carl Snell. There is more of interest to say about Snell than can fit into one talk, so I’ll restrict attention here to just this aspect of his thought: the role of the concept of "organic", and a contrast with "mechanical". Snell was a philosophical Romantic, influenced by Schelling and Goethe, and Kant’s Critique of Judgement. In Frege’s environment, the "organic/mechanical" contrast, understood Romantically, was a recognized cliché". More generally, Frege’s environment was more saturated with what we now call "Continental philosophy" than we might expect.
    This context-setting pays off for our reading of Frege’s texts: many turns of phrase that have been regarded as vague, throwaway metaphors turn out to be literal nods to familiar ideas in Frege’s environment. In particular, this is true of Frege’s account of "extending knowledge" via "fruitful concepts" and his rejection of a “mechanical” conception of arithmetic. When Frege appealed to "organic connection" and speaks of conclusions contained "like a plant in its seeds", he would have expected these phrases to have been understood in a very specific way.