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 : Frederic Jaeck (ENS), Nicolas Michel (Université d’Utrecht, Dpt de Mathématiques, & SPHere)
| Vers l’année en cours et les archives 2011– |
PROGRAMME 2020-2021
Nous nous réunirons en visioconférence, une fois par mois, de 16h à 18h sauf exception.
Les langues de travail seront le français et l’anglais.
Le contenu des séances sera annoncé progressivement au cours du semestre.
| lu 7/12/2020 | ma 12/01/2021 | ve 5/02 | ma 16/03 | ve 16/04 | ma 18/05 | ve 11/06 |
| Pour participer, le document support et le lien Zoom sont disponibles en écrivant à l’avance aux organisateurs : N. Michel ou F. Jaëck | ||||||
Lundi 7/12/2020, 16:00 – 18:00, visioconférence
- David Waszek (Université McGill)
‘Calculus’ as Method or ‘Calculus’ as Rules ? Boole against Frege on a systematic method for logic- Document support : la lecture préalable des extraits 1 & 2 est recommandée
Des traductions françaises sont également disponibles aux références suivantes :
. 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
- Document support : la lecture préalable des extraits 1 & 2 est recommandée
Mardi 12/01/2021, 16:00–18:00, visioconférence
- Discussion du groupe de travail sur la traduction du Bericht de Brill et Noether
Vendredi 5/02/2021, 16:00–18:00, visioconférence
- Bruno Belhoste (Université Paris 1)
Entre analyse et géométrie, l’approche de Monge
On examinera comment Monge a envisagé les rapports entre constructions géométriques et calcul algébrique dans sa recherche et son enseignement. On s’appuiera pour cela sur quelques exemples tirés de ses cours à l’École normale de l’an III et à l’École polytechnique.
Mardi 16 mars, 16:00–18:00, visioconférence
- Dirk Schlimm (Université McGill)
Discussion sur Boole & Frege on the aims of a logical calculus (suite de la séance du 7 décembre)
Vendredi 16 avril, !! 15:00 !!–18:00, visioconférence
- 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.
Mardi 18 mai, 16:00–18:00, visioconférence
- Nicolas Michel (Université d’Utrecht, Dpt de Mathématiques, & SPHere)
Intuition, calcul, et raisonnement. Philosophie et pratique de la géométrie chez Hieronymous Zeuthen
Vendredi 11 juin, 16:00–18:00, visioconférence
- 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.
