Quantum many body theory remains one of the frontiers of theoretical physics. Except for a handful of exactly solved models, most realistic problems remain hard to solve with any degree of control. One depends on computation intensive methods like diagonalisation of huge matrices, or quantum Monte Carlo, to obtain reliable answers. While `exact', these methods are severely size limited and hardly intuitive. I will provide a quick summary of how our intuition of quantum statistical problems has built up over the decades before encountering the current `strong correlation' situation. I will argue that an auxiliary field based approach that provides us with a coupled quantum-classical field theory at finite temperature is a natural starting point for these problems. This approach bypasses the exponential complexity of the parent many body problem and allows an intuitive connection to classical statistical mechanics and disordered (but non-interacting) quantum systems. An intractable problem gets mapped to two difficult but more familiar and manageable problems. Depending on the time available I can touch upon our results on the Mott transition and the BCS-BEC crossover.