He studied at Columbia College from 1944 to 1948, while on leave from the Coast Guard.
While sharing an office at Brookhaven National Laboratory, in 1954, Chen Ning Yang and Mills proposed a tensor equation for what are now called Yang–Mills fields. This equation reduces to Maxwell"s equations as a special case. See gauge theory.
Mills demonstrated his mathematical ability by winning the William Lowell Putnam Mathematical Competition in 1948, and by receiving first-class honors in the Tripos.
The mathematical ability he displayed there was evident throughout his career as theoretical physicist.
He earned a master"s degree from Cambridge, and a Doctor of Philosophy in Physics under Norman Kroll, from Columbia University in 1955. After a year at the Institute for Advanced Study in Princeton, New Jersey, Mills became Professor of Physics at Ohio State University in 1956.
He remained at Ohio State University until his retirement in 1995.