Dans le cadre du projet “les séries de problèmes, un genre au carrefour des cultures”, nous avons le plaisir de vous convier à une séance de séminaire où notre collègue américain Jeffrey Oaks, historien des mathématiques arabes, présentera le premier état de sa contribution au volume collectif que nous projetons de publier en 2014 (résumé du projet). M. Oaks étant invité par l’EHESS pendant le mois de mars, nous avons également inclus l’argument de ses autres conférences pour ceux d’entre vous qui êtes intéressé-e-s

Giovanna C., Alain B.

Series of problems in Arabic arithmetic and algebra

Mardi 4 mars, de 17h à 19h, salle 2, bâtiment Le France, séminaire de Giovanna Cifoletti.

 Algebra was just one of several methods for finding unknown numbers. Here I will draw examples from series of problems in the arithmetic and algebra books of al-Khwārizmī (early 9th c.), Abū Kāmil (late 9th c.), Ibn al-Yāsamīn (d. 1204), al-Ḥaṣṣar (late 12th c.), al-Fārisī (d. ca. 1320), the Latin translations Liber Mensurationum and Liber Augmenti et Diminutionis (12th c.), and others to show the form of these series, the standard wording of enunciations, and the various problem types.

Sur ce carnet on peut lire un billet de M. Oaks suite à son intervention sur l’algèbre d’al-Khawarizmi en 2012: “The series of problems in al-Khwārizmī’s Algebra” [X]

 AUTRES INTERVENTIONS DE M. OAKS EN MARS

Algebraic notation in medieval Arabic

Lundi 3 mars, de 17 h à 19 h, salle 015, RdC, bât. Le France, séminaire de Giovanna Cifoletti.

 Like most medieval books, Arabic books covering algebra read like transcriptions of lectures. This is due to the fundamentally oral nature of medieval Islamic civilization. Algebraic solutions to problems are written out in words, with no notation even for numbers. But problems were not solved rhetorically, of course. Algebraists would work out a problem in some kind of notation on a dust board or other ephemeral surface, and to record it in a book a rhetorical version of the calculations would be composed. From early texts it appears that only the coefficients of polynomials were written in Indian notation. But in the Maghreb in the twelfth century a notation specific to algebra developed in which the power was indicated also. This notation is not presented as a scientific development in the manuscripts, but is instead shown in textbooks to instruct students in its use. I will explain this notation and how it differs from modern notation.

Algorithms and creative thinking in medieval Arabic and Italian algebra

Jeudi 6 mars 2014, colloque ALGO – INHA, 2 rue Vivienne—6 rue des Petits champs, 75002 Paris / Salle VASARI (1er étage) 10 h 45 –11 h 45.

Polynomials and equations in Arabic algebra

25 mars de 17 h à 19 h, salle 2, bât. Le France, séminaire de Giovanna Cifoletti

 The medieval Arabic concepts of polynomial and equation differ from ours, and the structure of worked-out problems reflects this difference. The problems in Diophantus’ Arithmetica and in medieval European algebra point to the same premodern concepts. Examples from Diophantus, al-Karajī (early 11th c.), Maestro Biagio (1463), Bombelli (1572), and others will illustrate this.

Alain Bernard

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