From 1946, Yang studied in The University of Chicago, the adviser was Edward Teller(1908-2003), he received doctor's degree in 1948 and remained for a year as an assistant to Enrico Fermi. In 1949 he moved to the Institute for Advanced Study where he began a period of fruitful collaboration with Tsung-Dao Lee. In 1966 he moved to the State University of New York at Stony Brook and became the Albert Einstein Professor of Physics and the first director of a newly founded Institute for Theoretical Physics which is now known as C. N. Yang Institute for Theoretical Physics. He retired from Stony Brook in 1999 as Emeritus Professor.
He has been elected a Fellow of the American Physical Society, the Chinese Academy of Sciences(中国科学院, Beijing ), the Academia Sinica(中央研究院, Taiwan), the Russian Academy of Sciences, the Royal Society, etc. and was awarded an honorary doctorate by Princeton University (1958), Moscow State University (1992),Chinese University of Hong Kong(1997), etc.
Yang visited China mainland in 1971 for the first time after the thaw in China-US relation, after that he has made great efforts to help Chinese physics community to rebuild research atmosphere which was destroyed by the radical political movements. After retired from Stony Brook he returned as honorary director of Tsinghua University, Beijing, where he is the Huang Jibei - Lu Kaiqun professor at the Center for Advanced Study (CASTU).
Yang married Chih-li Tu a teacher, in 1950 and has two sons and a daughter: Franklin Jr., Gilbert, and Eulee (in order of age). His father-in-law was the Kuomintang General Du Yuming. His wife died in the winter of 2003. At the age of 82, Yang became engaged to 28-year old Weng Fan who was studying for her master's degree at Guangdong University of Foreign Studies. They married in early 2005.
In The University of Chicago, Yang first spent twenty months in an accelerator lab to work on experiment, but he later found he was not quite good at experiment and switched back to theory. His Doctor thesis was about angle distribution in nucleon reaction, later he worked on particle phenomenology, a well known work was Fermi-Yang model treating Pion meson as bound state of nucleon-antinucleon pair. In 1956, he and Tsung-Dao Lee proposed that in the weak interaction the parity symmetry was not conserved, the research team of Chien-Shiung Wu at the National Bureau of Standards in Washington experimentally verified the theory. Yang and Lee received the 1957 Nobel Prize in Physics for their parity violation theory. Yang has also worked on neutrino theory(with T.D.Lee, 1957, 1959), CT nonconservation(with T.D.Lee and R.Oheme, 1957), electromagnetic interaction of vector mesons(with T.D.Lee, 1962), CP nonconservation(with Wu Tai-Tsun, 1964).
Yang is also well known for his collaboration with Robert Mills in developing non Abelian gauge theory, widely known as the Yang-Mills theory. Such "Yang-Mills theories" are now a fundamental part of the Standard Model of particle physics. In the 1970s Yang worked on the topological properties of gauge theory, collaborated with Wu Tai-Tsun they elucidated the Wu-Yang monopole, unlike Dirac monopole, it has no singular Dirac string. Gauge theory turns out to be related with fiber bundle in mathematics and has been an important research subject since 1970s.
Yang has a great interest in statistical mechanics since his undergraduate era, in the 1950s and 1960s, collaborated with Tsung-Dao Lee and Kerson Huang, etc. he studied statistical mechanics and condensed matter theory. He studied theory of phase transition and elucidated the Lee-Yang circle theorem, properties of quantum boson liquid, two dimensional Ising model, flux quantization in superconductors(with N. Byers, 1961), proposed the concept of Off-Diagonal Long-Range Order(ODLRO, 1962). In 1967, he found a consistent condition for a one dimensional factorized scattering many body system, the equation was later named Yang-Baxter equation, it plays an important role in integrable models and has influenced several branches of physics and mathematics.