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(Re)-Investigating and Comparing "Series of Problems" - Athens, 2014 MITHe-CAK Workshop

This workshop explores the definition, diachronic value, cultural history, and purpose of mathematical commentaries and series of problems, including a focus on the significance of paraphrasis in Diophantus's Arithmetica.

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(Re)-Investigating and Comparing "Series of Problems" - Athens, 2014 MITHe-CAK Workshop

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  1. (re)-investigating and comparing “series of problems” Alain Bernard, Centre A. Koyré Sat 11th, 2014. Athens, MITHe-CAK workshop Comparing mathematical commentaries and series of problems from antiquity to early modern times: how and for what purpose?

  2. Main points • The roots of the SoP project • Re-investigating "series of problems" • 2.1 what is is + why we had to publish • 2.2 revising the introduction of the SoP 2014 volumea/ definition b/ diachronic value c/ cultural history d/ inventory e/ goal • (hence) some final words about paraphrasis in Dipohantus

  3. The roots of the SoP project • (a shelter for) interdisciplinary research • Political need  collaborations around projects • Intellectual need  looking for backgrounds and points of comparison • Building a framework for diachronic studies • Building a bridge between educational issues, teacher training, and historical research.

  4. Re-investigating series of problems2.1 what it is? why publish? • What it was, what it became, what it is: • Initial argument [] • Growing bigger 2011  2014 [] • Difficulties in keeping available for the project • Publishing as an alternative to (sad) death • Temporary success (?): • Around 14 contributions coming in • New project launched for 2015 []

  5. Re-investigating series of problems2.2 revising the core argt= DEFINITION • (voluntarily) defining a “flabby” object  SoP = object of discussion and re-appropriation • … though not completely flabby: • Not separable from a general problem of categorisation, SoP = a genre • SoP are texts including materiality. • “problems / questions” are generic  but textual entities, with pb of recognition • “questions and answers” are also generic  looks like the medievists’ category, but broader

  6. Re-investigating series of problems2.2 revising the core argt = SERIALITY • Aurélien’s question on the meaning of series. • A particular question = what is order without order? • A general question = how should it be understood? • What is seriality? Intentional order? Or recognizable bond / ‘textual sequence’? • Three (non separable?) ways to understand seriality (a) as our own product, (b) as historio-graphical products (c) as actors’ categories. • (defining) Intentionality calls to cultural history

  7. Re-investigating series of problems2.2 revising the core argt = STABILITY? • A traditional idea among historians of mathematics and folklorists = problems have a long span, subject to oral transmission, etc. • SoP meant as a critical approach to this idea • Is there then a positive idea of “stability” for SoP? • Stable forms? (C. Macé) • Instable forms with recomposition (BV and MM?)? • Or need to reformulate the basic idea in terms of “vitality” of forms and contents? (IV)

  8. Re-investigating series of problems2.2 revising the core argt = CULTURAL HISTORY • Cf. discussion on “intentional seriality”  intentions defined by inquiries into culture • Situating the activity of “problematizing” in historical context • The role of SoP in the constitution of communities, esp. of practitioners, teachers and specialised “scientists”

  9. Re-investigating series of problems2.2 revising the core argt = INVENTORY, EDITION, MODELS • A clear need for inventories in some contexts = arabic mathematics, medieval QRs, etc. • What categories should be built for this? • Even for studying a single text, what categories, what model of understanding should be developed? • The two last approaches related to modelisation in “DH” sense

  10. Re-investigating series of problems2.2 revising the core argt = GOAL • Putting emphasis on new results and perspectives • example of the role of paraphrase • New ways to investigate corpuses • An opening toward the detailed reading and study of texts? • Building sub-themes? But the object is at their crossroad  interesting problem []

  11. 3. What about paraphrasein Diophantus’sArithmetica? • The ‘oakian’ principle and idea of coloring terms within statements and solutions [x] • Basic idea = to adapt the technique to D’s Arithm[x],and show the centrality of paraphrase in D’s technique of solution • Potential developments of this work: • Sustaining a new interpretation of the preface • Situating D’s work in a larger corpus = comparative tool • Reading D through the prism of rhetorical paraphrasis

  12. The contributors to the SoP project • Within HASTEC laboratories • S. Lamassé(IHMC) / G. Cifoletti, A. Bernard, J. Peiffer(CAK) / B. Vitrac, A. Berra (ANHIMA) / I. Ventura (IRHT) • Associates, partners • G. Chambon (UBO) / J. Christianidis(Univ. Athens, ass. CAK) / M. Moyon(Univ. Limoges, ass. CAK) / J. Oaks(univ. Indianapolis) / U. Kundert (Wolfenblütel) / C. Macé (Leuvens) • Students: • F. Aceto (doct. GAHOM) / K. Gosztonyi (doct. univ. de Szeged)/ A. Megremi(Univ. Athens) / F. Bantaba, J.M. Coquard, C. Serra (CAK)

  13. Ancient MesopotamianCorpus (GC) Texts /corpuses Heronian and pseudo-heronian metrological corpus (BV) Patristic literature (CM) Parts of the Palatine Anthology and of Deipnosophisteis(Au B) « Playing with infinity », R. Péter 1943 (KG) Diophantus’s Arithmetica (Al. B, JC) Collection of problems in ‘Journaux Savants’ (JP) Medieval texts on metrology and measurement (MM) 17th cent coll. of disputationes (UK) Medieval Byzantine Quadrivia (JC, NM) Medieval arithmetics (SL) Medieval texts of algebra (JO) Renaissance arithmetics + algebraic treatises (GC) Medevial encyclopedia texts in the form of Questions and Answers, MA and Renaissance (IV)

  14. SoP: the initial argument • Considering any text made of questions and answers and following some kind of seriality • Four reasons to study them: • (apparent) diachronic stability • Subject for cultural history • Need for inventories and editions • Problems of historiography and categorisation • A goal: gaining new points of view by crossing “cultural perspectives” on them

  15. Initial argument Def + reasons + goal Amplified argument (new) Def + reasons + goal C1 Cn BEGINNINNGS  WHERE WE ARE  WHERE WE GO C… C3 C2 C5 C7 C6 C4 Subtheme 1 T1.1 – T1.2 – T1.3 – T1.4 Gen intr T2.1 – T2.2 – T2.3 – T2.4 Subtheme 2 SOURCEBOOK Subtheme n Tn.1 – Tn.2 – Tn.3 – Tn.4

  16. Program of 2015 seminar • Feb 12th : S. Lamassé (IHMC), Circulation de séries de pro-blèmes mathématiques dans un contexte universitaire.   • March : Iolanda Ventura (IRHT), Lecture de séries de problèmes à caractère encyclopédique. • End of May  : Aurélien Berra (ANHIMA), Lecture de séries de problèmes lettrés et ludiques. • June : Giovanna Cifoletti (Centre A. Koyré), Lecture de séries de problèmes de la Renaissance aptes à former du point de vue juridique les mathématiciens et les juristes. • Nov : Marc Moyon (associé Centre Koyré) + Bernard Vitrac (ANHIMA), Lecture de séries de problèmes métrologiques.

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