His next job was at Yale University, where he remained for most of the rest of his life, retiring in 1972. At Yale, it was discovered that he had never received a Ph.D. The Norwegian Institute of Technology found that his his work in reciprocal relations was too incomplete to qualify as a doctoral dissertation. Yale said they would accept one of his published papers instead, but Onsager insisted on doing a new research project. His dissertation, called "Solutions of the Mathieu equation of period 4 pi and certain related functions", was too hard for the chemistry and physics faculty to understand. It was only after the mathematics department said they would give him the doctorate instead, that he was granted a Ph.D. in chemistry in 1935. He was appointed assistant professor in 1934, and associate professor in 1940. At Yale he produced brilliant theoretical research, but could not teach or explain ideas to students. He was also unable to direct the research of graduate students, except for the occasional outstanding one.