ADM mass proves useful in analysis of asymptotically flat spacetimes, although the study of the notion itself was not devoid of difficulties. A good example here is the question of positive definiteness of this quantity, which had to wait over twenty years for a decisive answer. The talk will consist of a short historical review of main methods used to approach the problem, followed by a presentation of an alternative proof of positive-energy theorem, based on elementary tools of differential geometry only.