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Séminaire – Mathématiques 19e-21e, histoire et philosophie
avril 12 @ 14h00 - 17h30
Dirk Schlimm (McGill University)
Notations, calculations, and proofs
Résumé :
Studying the role of signs (e.g. notations or figures) in mathematical practice can be a way to gain insight into how human computational constraints shape our mathematical theories (see Waszek 2023). I investigate the role of signs—also called ‘representations’—in the context of the recently developed theory of cluster algebras. Within this theory, one finds different forms of representations which are used to encode the ‘same’ information. While such representations are considered to be equivalent, I argue that they differ in terms of the support they provide for visualizing both the relations which they encode and the transformations which are defined on them. Moreover, we can examine the specific contexts in which these representations appear and the aims which they are intended to be used for in order to better understand their epistemic and pragmatic roles. This case study also offers opportunities for considering which transformations or operations may count as computations.
Mary Louise Elworth (Aarhus University)
Computation or mutation ? Cluster algebras as a case study
Résumé :
Studying the role of signs (e.g. notations or figures) in mathematical practice can be a way to gain insight into how human computational constraints shape our mathematical theories (see Waszek 2023). I investigate the role of signs—also called ‘representations’—in the context of the recently developed theory of cluster algebras. Within this theory, one finds different forms of representations which are used to encode the ‘same’ information. While such representations are considered to be equivalent, I argue that they differ in terms of the support they provide for visualizing both the relations which they encode and the transformations which are defined on them. Moreover, we can examine the specific contexts in which these representations appear and the aims which they are intended to be used for in order to better understand their epistemic and pragmatic roles. This case study also offers opportunities for considering which transformations or operations may count as computations.
Lieu : Salle Malevitch 483A bâtiment Condorcet – Université Paris Cité
