When the discovery of Quantum Mechanics revolutionized the Newtonian conception of Physics at the beginning of the 20th century, important mathematical developments helped to boost this revolution. Even by now not all of the possible consequences of this discovery have been understood and applied. The range of prospects appears to be fantastic. Current important applications range from the research of new pharmaceutical molecules to the conception of revolutionary computers working on a completely different physical basis or the creation of totally new materials. And cutting edge Mathematics continues to accompany Quantum Mechanics and the theories born from it in their way toward progress for our societies.