A simple mathematical model has been proposed by biologists to describe the feedback mechanism used by the Physarum Polycephalum slime mold to adapt its tubular channels while foraging two food sources A and B. In this talk I will sketch a proof of the fact that, under this model, the mass of the mold will eventually converge to the shortest A-B path of the network that the mold lies on, independently of the structure of the network or of the initial mass distribution. This will be a whiteboard talk.