Entre géométrie et théorie des substitutions  : une étude de cas autour des vingt-sept droites d’une surface cubique

Lê, François

doi:10.5802/cml.2

Cited by 7 publications

(7 citation statements)

References 21 publications

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“…See (Ehrhardt, 2012, 173-182) for an analysis of Jordan's works on Galois theory and (Brechenmacher, 2011) for more general relations between Jordan and Galois. 56 See (Lê, 2013) for explanations about the mathematical content of the Traité and a discussion of the relations between the theory of substitutions and geometry around the twenty-seven lines equation. 57 Jordan always used relations that were already known.…”

Section: Jordan and The Traité Des Substitutions Et Des éQuations Algmentioning

confidence: 99%

“Geometrical equations”: Forgotten premises of Felix Klein's Erlanger Programm

Lê

2015

Historia Mathematica

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Felix Klein's Erlanger Programm (1872) has been extensively studied by historians. If the early geometrical works in Klein's career are now well-known, his links to the theory of algebraic equations before 1872 remain only evoked in the historiography. The aim of this paper is precisely to study this algebraic background, centered around particular equations arising from geometry, and participating on the elaboration of the Erlanger Programm. Another result of the investigation is to complete the historiography of algebraic equations, in which those "geometrical equations" do not appear. RésuméLe Programme d'Erlangen de Felix Klein (1872) a été abondamment étudié par les historiens. Si les premiers travaux géo-métriques de la carrière de Klein sont maintenant bien connus, ses rapports à la théorie des équations algébriques antérieurs à 1872 ne sont qu'évoqués dans l'historiographie. Le but de cet article est justement d'étudier ce contexte algébrique, centré autour d'équations algébriques particulières provenant de la géométrie, qui participe à l'élaboration du Programme d'Erlangen. Un autre résultat de ce travail est la complétion de l'historiographie des équations algébriques, dans laquelle ces "équations de la géométrie" n'apparaissent pas.

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Section: Jordan and The Traité Des Substitutions Et Des éQuations Algmentioning

confidence: 99%

“Geometrical equations”: Forgotten premises of Felix Klein's Erlanger Programm

Lê

2015

Historia Mathematica

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“…9 Vgl. Lê [11] 16 Die didaktische Verwendung von Modellen, also ihr Einsatz in der Lehre, schimmert an vielen Stellen des vorliegenden Werkes durch, allerdings ohne konkrete Hinweise, wie das geschehen ist. Auch Brills Diktum, ihm seien die Modelle in der Lehre unentbehrlich geworden 17 , gibt hierüber leider keine Aufschlüsse.…”

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“…Tobies-Volkert[14, S. 127-134]. Die Société Mathématique de France hatte sich 1872 in der Nachfolge des Deutsch-Französischen Krieges gegründet 11. ETH-Bibliothek, Hochschularchiv, Hs 87: 1495, Brief von Weiler aus Göttingen an Fiedler vom 20.…”

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Ernst Seidl, Frank Loose und Edgar Bierende (Hrsg.): Mathematik mit Modellen

Volkert

2020

Math Semesterber

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Mathematische Modelle hatten in den letzten Jahren ohne Zweifel Konjunktur, wie auch mehrere Artikel in den "Semesterberichten" belegen. 1 Wurden vor 50 Jahren Assistentinnen und Assistenten damit beauftragt, diese verstaubten Objekte zu entsorgen, so schwärmten sie in den letzten Jahren aus, um solche in Kellern und Speichern wieder aufzustöbern. Die mehr oder minder zahlreichen Fundstücke wurden restauriert, fotografiert und im Internet präsentiert.

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“…My own research led me to confront these categories while I was studying a precise historical question: the introduction of equation theory and substitution theory into geometry during the second half of the nineteenth century. To be more specific, this research brought to light the importance of “geometrical equations,” objects which have proved absolutely crucial for the understanding of encounters between those three mathematical domains around 1870 (Lê 2015a; Lê 2015b). A special feature of “geometrical equations” is that they gave rise to precise technical activities shared by a few mathematicians over a quite short period of time, although they were not well-defined mathematical objects.…”

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confidence: 99%

“… 21 With the same procedure, I added a few other texts listed in the Répertoire bibliographique des sciences mathématiques , another project at the end of the nineteenth century aimed at inventorying mathematical production. More details on the selection process can be found in Lê 2015b. For the Répertoire , see Nabonnand and Rollet 2002. …”

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Reflections on the Notion of Culture in the History of Mathematics: The Example of “Geometrical Equations”

Lê

2016

Sci Context

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Argument This paper challenges the use of the notion of "culture" to describe a particular organization of mathematical knowledge, shared by a few mathematicians over a short period of time in the second half of the nineteenth century. This knowledge relates to "geometrical equations," objects that proved crucial for the mechanisms of encounters between equation theory, substitution theory, and geometry at that time, although they were not well-defined mathematical objects. The description of the mathematical collective activities linked to "geometrical equations," and especially the technical aspects of these activities, is made on the basis of a sociological definition of "culture." More precisely, after an examination of the social organization of the group of mathematicians, I argue that these activities form an intricate system of patterns, symbols, and values, for which I suggest a characterization as a "cultural system."

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Entre géométrie et théorie des substitutions : une étude de cas autour des vingt-sept droites d’une surface cubique

Cited by 7 publications

References 21 publications

“Geometrical equations”: Forgotten premises of Felix Klein's Erlanger Programm

“Geometrical equations”: Forgotten premises of Felix Klein's Erlanger Programm

Ernst Seidl, Frank Loose und Edgar Bierende (Hrsg.): Mathematik mit Modellen

Reflections on the Notion of Culture in the History of Mathematics: The Example of “Geometrical Equations”

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