This article records tradition as it has been passed down and reported. Its sources are not yet part of the atlas's verified catalogue.
When Chen-Ning Yang and Robert Mills published their three-page paper in Physical Review in October 1954, hardly anyone noticed. Conservation of Isotopic Spin and Isotopic Gauge Invariance proposed a striking generalization: what if the local symmetry that Maxwell's electromagnetism obeys, the freedom to redefine a particle's phase differently at every point in space and time, could be extended to symmetries with more than one direction, the kind that describe a proton and a neutron as two states of a single particle?
The mathematics worked, but physics seemed to punish it. Yang-Mills theory predicted force-carrying particles with zero mass, the way the photon is massless, yet no massless carriers of the strong or weak force had ever been observed. Wolfgang Pauli had explored a similar idea privately a year earlier and abandoned it for the same reason. When Yang gave a seminar on the new theory at Princeton in late February 1954, eight months before the paper was published, Pauli pressed him directly from the audience, asking "What is the mass of this field?" twice and dismissing Yang's answer that it was an unresolved, complicated problem as "not sufficient excuse", an exchange sharp enough that Yang sat back down before finishing. For most of the next two decades, Yang-Mills theory sat at the edge of theoretical physics: elegant, admired by a small circle, and apparently disconnected from anything an experiment could see.
The resolution came in pieces during the late 1960s and 1970s. The Higgs mechanism showed how a Yang-Mills field's carriers could acquire mass without breaking the underlying symmetry, opening the door to the electroweak theory that unifies electromagnetism with the weak force. Around the same time, the discovery of asymptotic freedom showed that quarks, bound by a Yang-Mills field of their own, interact more weakly at short distances, exactly the property needed to make sense of the strong nuclear force as quantum chromodynamics. By the time the Standard Model of particle physics reached its modern form, Yang-Mills theory was not a curiosity at its margins but the grammar the whole theory was written in.
The theory has since outgrown physics. Mathematicians studying the existence and structure of Yang-Mills fields on general geometric spaces helped found much of modern gauge theory in mathematics, and the Clay Mathematics Institute named the Yang-Mills existence and mass gap problem, whether the theory's particles genuinely have the mass their observed behavior implies, one of its seven Millennium Prize Problems in the year 2000. It remains unsolved.