Savoirs mathématiques et arts de penser à l'époque moderne

Thèmes de recherche :

• Maîtres d'abaque, algébristes et juristes du Moyen Age à l'époque moderne : de l'expérience à l'écriture, de la technique à la théorie.

•  Langue algébrique et algorithme: art de penser, machines à penser et pensée des machines» (en co-coordination avec Massimo Mazzotti du (CSTMS, UC Berkeley) financé par le « Grant Award France-Berkeley Fund.

• Le nombre entre cognition, anthropologie et histoire (projet international)

• Mathématiques et rhétorique. La rhétorique art de penser de l'antiquité à l'époque moderne.

Projet de recherche et d'enseignement :

• Maîtres d'abaque, algébristes et juristes du Moyen Age à l'époque moderne : de l'expérience à l'écriture, de la technique à la théorie.

•  Langue algébrique et algorithme: art de penser, machines à penser et pensée des machines» (en co-coordination avec Massimo Mazzotti du (CSTMS, UC Berkeley) financé par le « Grant Award France-Berkeley Fund.

• Le nombre entre cognition, anthropologie et histoire (projet international)

• Mathématiques et rhétorique. La rhétorique art de penser de l'antiquité à l'époque moderne.

Evenements

PRACTICE AND SENSE IN 16th-CENTURY MATHEMATICS
EXAMPLES FROM ITALY AND KERALA
international workshop.-atelier en  ligne  14 et   16  avril 2020

 The nature of numbers and diagrams in and around Bombelli's algebra

Rafael Bombelli’s L’algebra (1572) was published in the context of the Italian algebra practiced by abbacus masters and Renaissance mathematicians of the 14th–16th centuries: we will focus  on the semiotic aspects of algebraic practices and on the organization of knowledge, to show how symbols that stand for underdetermined meanings combine with shifting principles of organisation to change the character of algebra.
Despite Bombelli’s careful adherence to a form of homogeneity, he constructs several different ways of relating algebra and geometry, building on Greek, Arabic, abbacist and original approaches. Bombelli’s technique of reading diagrams, especially when representing algebraic unknowns, requires a multiple view that makes lines stand for much more than the diagrams present to an untrained eye.

 Three case studies of late medieval south-Indiam mathematics

Sanskrit and Malayalam versions of Citrabhānu’s Twenty-One problems isa discussion of quadratic and cubic problems from 16th-century Kerala.

Kriyākramakarīis a16th century Sanskrit mathematical treatise, a commentary on Bhāskara II’s twelfth-century Līlāvatī, one of the most famous mathematical treatises of the Sanskrit mathematical tradition. The Līlāvatī covers all standard areas of Sanskrit arithmetic and geometry, from the most elementary calculations to advanced procedures, up to but excluding algebra and trigonometric tables  The purpose of proofs in the Kriyākramakarī is, among other things, to connect various different aspects of mathematics, rather than just to convincingly establish or explain mathematical claims by means of previously known claims.

Kanakkatikāram  is a genre of treatises for teaching practical mathematics beyond the level of basic arithmetic that disseminated in late medieval and early modern South India in Kerala and Tamil Nadu.