# Why hasn't Peter Higgs solved the Yang-Mills prize problem?

The Higgs mechanism gets rid of the mass gap problem, and it's been experimentally proven, so why is there still a problem?

• Well it's an objective decision from the people who give out the million dollars. What's their reasoning? – user250721 Feb 3 at 3:17
• Have you read this description of the problem? “For example, in the case of G=SU(3)—the strong nuclear interaction—the winner must prove that glueballs have a lower mass bound, and thus cannot be arbitrarily light.” Does that follow from Peter Higgs’ work? I don’t think it does. – G. Smith Feb 3 at 4:33
• In what way do you imagine that the Higgs mechanism "gets rid of the mass gap problem"? – Martin C. Feb 3 at 16:49

Prove that for any compact simple gauge group G, a non-trivial quantum Yang–Mills theory exists on $$\mathbb{R}^{4}$$ and has a mass gap $$\Delta > 0$$. Existence includes establishing axiomatic properties at least as strong as those cited in Streater & Wightman (1964), Osterwalder & Schrader (1973) and Osterwalder & Schrader (1975).