Yang-Mills existence and mass gap

The Yang-Mills existence and mass gap problem is a fundamental question in physics and mathematics. It asks whether the equations describing certain force fields—like those that bind particles in atomic nuclei—are mathematically consistent and whether these fields naturally produce particles with a positive mass (a "mass gap"). Proving existence ensures the theories make sense, and showing a mass gap explains why some particles are massive while the underlying forces are mediated by massless fields. Solving this would deepen our understanding of the universe's fundamental forces and confirm the validity of important parts of quantum physics.