Witten's proof of the positive energy theorem

Unlike Newtonian gravity, where systems can have arbitrarily negative energies due the gravitational potential's negativity, a remarkable property of general relativity is the positivity of the total energy. Over time, this fact has been proven via a number of methods, with varying generality. The simplest strategy by far was invented by Witten in 1981. The proof's elegance and surprising use of the Dirac equation were cited among the reasons for awarding Witten the Fields Medal. After some opening remarks on defining energy in general relativity, the main portion of my talk will be devoted to presenting Witten's proof. Time permitting, I will conclude by discussing variations and generalisations.