In mathematical physics, the Yang–Mills existence and mass gap problem is an unsolved problem and one of the seven Millennium Prize Problems defined by the Clay Mathematics Institute, which has offered a prize of US$1,000,000 to the one who solves it. The problem is phrased as follows: In this statement, a Yang–Mills theory is a non-abelian quantum field theory similar to that underlying the Standard Model of particle physics; R 4 {displaystyle mathbb {R} ^{4}} is Euclidean 4-space; the mass gap Δ is the mass of the least massive particle predicted by the theory.