New mathematical principles, involving the quantum field theory of many body systems, are required to understand the collective behavior of matter on diverse scales. The Rutgers group has pioneered some of these new methods - with the development of the scaling theory of localization in metals, the first exact solution of the Kondo model, the development of new methods for exploring ferroelectricity and hydrogen bonds with density functional theory, the invention of the slave boson method and dynamical mean field theory.