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Axis History and philosophy of mathematics

Mathematics 19th – 21st, History and Philosophy

The seminar on the history and philosophy of modern mathematics is a place of presentation and discussion of mathematical texts produced in the 19th and 20th centuries, in both historical and philosophical perspectives. It intends to serve as a place of exploration (reading, translation, explanation) of mathematical documents little or poorly known, but also to present work in progress on these periods. The emphasis is on proximity to textual sources. The sessions usually take the form of a discussion of the said sources (to which speakers give prior access), preceded by a historical or mathematical exposition.

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

2011-2012, 2012-2013, 2013-2014,
2014-2015, 2015-2016, 2017-2018,
2018-2019, 2019-2020, 2020-2021

PROGRAM 2021-2022

We will meet by webconference first, then at the Université de Paris* once a month on Mondays, except for Tuesday June 14.
Languages will be French and English.
Details of sessions will be displayed during the semester.
* 4, rue Elsa Morante, Building Condorcet, 75013 Paris (access map)

10/25/2021, 3pm–5pm 11/15, 5pm–7pm 12/13, 3pm–5pm 01/24/2022, 2pm–4pm 02/21, 2pm–4pm
03/14, 2pm–4pm 04/04, 2pm–4pm 05/23, 2pm–4pm 06/14, 2pm–4pm
To participate online, thanks to write to the organizers:
N. Michel or F. Jaëck for the document and the link Zoom

Monday October 25th 2021, 3pm – 5pm, webconference
  • Sara Confalonieri (HPS, University of Paris, SPHere)
    La méthode de Fourier pour dénombrer et séparer les racines réelles: "Et je l’ai résolue par une méthode exacte et générale"
    Le théorème de Sturm (1829) sur le dénombrement des racines réelles d’un polynôme réel eut une grande résonnance. L’exposé examine la méthode de Fourier (1787-1831) qui est la source d’inspiration explicitement déclarée par Sturm, d’un côté en visant à une remise en contexte à plusieurs niveaux (interactions avec la règle des signes de Descartes ainsi qu’avec le plus ample contexte des discussions sur les nombres complexes), et de l’autre côté en formulant des hypothèses sur sa réception manquée.

Monday November 15th 2021, 5pm – 7pm, Room 646A & webconference

  • ! cancelled ! Norbert Schappacher (Université de Strasbourg)
    A “Revolution” in Mathematical Practice? Reflections on the Introduction of Cohomological Methods.

Monday December 13th 2021, 3pm – 5pm, Room 646A & webconference

  • Sébastien Gandon (Université Clermont-Auvergne)

Monday January 24, 2022, 2pm – 4pm, Room 646A & webconference

  • Tom Hedley (Trinity College Dublin)
    Killing the Pope: Hausdorff, Nietzsche and the Modern(ist) Language of Mathematics
    A few months before his inaugural lecture on the problem of space at the Universität Leipzig in 1903, Felix Hausdorff released one of his last (and most extensive) essayistic works under his pseudonym, Paul Mongré, entitled “Sprachkritik” (Critique of Language). The role and influence of Nietzsche and the Eternal Return in Hausdorff/Mongré’s earlier philosophical works and his turn to Cantor’s set theory has in recent years received due scholarly attention, but by 1903, Mongré seemed to distance himself from Nietzsche’s latter-day fanaticism. On the face of it, the subject of Mongré’s Sprachkritik is the Vienna-based language theorist Fritz Mauthner, whose own critique of language is paralysed by the central paradox that one has to use language itself to critique it — a predicament Mauthner compares to the Pope accidentally killing himself when he tries to eradicate his bedbugs. In his essay, Mongré rises above Mauthner’s pessimistic stance and turns to mathematics as the language that can outwit this paradox. His turn, however, can only be explained by his lingering indebtedness to Nietzsche, this time his fiery (and surprisingly brief) language criticism in “Über Wahrheit und Lüge im außermoralischen Sinne”. In this talk, I will explore how Nietzsche too, his bloodlust unsatisfied by famously killing God in the 1880s, had to insist on the death of the Pope in order to unshackle artistic creativity in language, and I will ask how Mongré was able to draw on this twist to arrive at mathematics as free, creative thought par excellence.

Monday February 21, 2pm – 4pm, Room 646A & webconference

Monday March 14, 2022, 2pm – 4pm, Room 646A & webconference

Monday April 4, 2pm – 4pm, Room 646A & webconference

Tuesday May 23, 2pm – 4pm, Room 646A & webconference

Monday June 14, 2pm – 4pm, Room 646A & webconference