As is well known a strong interaction exists between Geometry & Art since the antiquity. This interaction has been revitalized by the developments of new artistic sensibilities in XX Century up to the turn of the third Millennium. Starting from the revolutions of Impressionism, Cubism and Futurism we discuss the role that Mathematics, Science and Technology had in inspiring some artistic movements: more specifically Geometric Abstractism, Constructivism, Kinetic Art and Optical Art. Particular attention will be given to the work of Vasily Kandinskii, Max Bill, Alexander Calder and Milan Dobes; we shall shortly mention also the role that Relativity, Quantum Mechanics and Gestalttherie have played in early XX Century in forming these new sensibilities on perceiving and representing ``reality''. In this way we shall emphasize that to understand most of the new forms of Art developed in the past Century one needs to understand (or at least grasp) their mathematical and technological roots.