We present, from an epistemological point of view, the evolution of physical concepts in the context of the relation between mathematics and physics. We stree the importance of symmetries and of space-time in fundamental physical theories and show that the above evolution is best understood in the framework of the mathematical notion of deformation. Important paradigms include the concepts of relativity and of quantization, exemplified by deformation quantization and its manifold avatars going from analytic and algebraic geometry to quantum groups and the "dual" aspect of quantum spaces. Deforming Minkowski space-time and its symmetry to anti de Sitter has significant physical consequences that we sketch. We end by presentin an ongoing program in which anti de Sitter would be quantized in some regions, speculating that this might explain baryogenesis in a universe in accelerated expansion. All this relates to major contributions by IHES professors in the past 50 years, and hopefully in the coming 50 years.
By Tohru Eguchi
By Eliezer Rabinovici
By Daniel Sternheimer
By Erik Verlinde
By Thibault Damour
By Niklas Beisert
By Ludwig Faddeev
By Nathan Berkovits
By Hermann Nicolai
By Dirk Kreimer
By Keiji Oguiso
By Ngaiming Mok
By Olivia Caramello , Jérémie Bouttier
By Olivia Caramello , Mateo Carmona , Francesco La Mantia , Charles Alunni , Dominique Lepetz
