The mass gap is well established by physics experiment and by computer simulation, but no one has derived it as a mathematical consequence of the quantum Yang-Mills equations themselves, and no fully rigorous construction of a four dimensional quantum Yang-Mills theory yet exists.
What would resolve this A rigorous mathematical construction of quantum Yang-Mills theory on four dimensional space for a compact simple gauge group, together with a proof that it has a mass gap greater than zero.
OpenMathematical physicsClay Mathematics Institute