We review our recent measurements of the complex AC conductivity of thin InO_x films studied as a function of magnetic field through the nominal 2D superconductor-insulator transition. These measurements - the first of their type to probe nonzero fre
quency - reveals a significant finite frequency superfluid stiffness well into the insulating regime. Unlike conventional fluctuation superconductivity in which thermal fluctuations give a superconducting response in regions of parameter space that dont exhibit long range order, these fluctuations are temperature independent as T --> 0 and are exhibited in samples where the resistance is large (greater than 10^6 Ohms/Square) and strongly diverging. We interpret this as the direct observation of quantum superconducting fluctuations around an insulating ground state. This system serves as a prototype for other insulating states of matter that derive from superconductors.
