After an epistemological introduction on "mathematics and physics, two communities separated by a common language" and the three questions that a scientist should consider (why, what and how) we look at the paradigm of quantization. For us it is an instance of the deformation philosophy of Flato and not necessarily a functor between categories of algebras as in most "mathematizations" of the Copenhagen interpretation. We then present the mathematical and physical background and give a tachyonic overview of deformation quantization and of its "avatars" (including noncommutative geometry, quantum groups and quantized spaces). We end by speculations around a possible "quantized anti de Sitter" structure in the universe when both deforming and quantizing our Mnkowski space-time.