<p>The goal of this short note, written to mathematicians and mathematical physicists, is to give a brief description of one of the Clay Foundation one-million dollar problem. Namely, in relatively simple terms, we state what the mass gap problem is for the quantum field theory model called pure Yang-Mills theory in four Euclidean spacetime dimensions. In this context, after a historical survey of the field, we introduce the model, we explain why it is an important piece in the physics of interacting elementary particles and we set up the problem.</p>