Yang-Mills-Millennial problem

The Yang-Mills Millennium Problem asks whether, in the context of quantum physics, certain mathematical equations called Yang-Mills theories always have a well-defined, stable solution, or "mass gap." These theories describe the fundamental forces like the strong nuclear force. Mathematically, the challenge is to prove whether solutions exist that explain how particles acquire mass without relying on external mechanisms. Solving this problem would confirm key ideas in physics and provide a deeper understanding of the universe’s fundamental forces. It remains one of the seven Clay Mathematics Institute's major unsolved problems, with a $1 million prize for a solution.