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Yang-Mills theory

A mathematical framework physicists use to describe the forces that hold atomic nuclei together.

Yang-Mills theory is a set of equations that describes how particles interact through certain fundamental forces, including the strong force that binds the nucleus of an atom. It is a cornerstone of the Standard Model, the best current theory of particle physics.

Physicists use it successfully every day, but mathematicians have never fully proven that it is consistent in the real four-dimensional world. Closing that gap is one of the Millennium Prize Problems.