"Institute for Advanced Study in Princeton" is a top research center in physics and math. Yang worked there for 16 years, before he moved to Stony Brook University, which was then a newly founded university and was eager to appoint some famous professors. Yang was named the Albert Einstein Professor of Physics and the first director of the newly founded Institute for Theoretical Physics. Today this institute is known as the C. N. Yang Institute for Theoretical Physics.
To be honest, and Yang's level, he did not need to be affiliated to any university to prove himself anymore. Universities need prestigious professors like him.
