became apparent during the decades following World War II, and by 1968 they were considered important enough to gain Onsager that year's Nobel Prize in Chemistry. In 1933, just before taking up the position at Yale, Onsager traveled to Austria to visit electrochemist Hans Falkenhagen. He met Falkenhagen's sister-in-law, Margrethe Arledter. They were married on September 7, 1933, and had three sons and a daughter. Yale University At Yale, an embarrassing situation occurred: he had been hired as a postdoctoral fellow, but it was discovered that he had never received a Ph.D. While he had submitted an outline of his work in reciprocal relations to the Norwegian Institute of Technology, they had decided it was too incomplete to qualify as a doctoral dissertation. He was told that he could submit one of his published papers to the Yale faculty as a dissertation, but insisted on doing a new research project instead. His dissertation laid the mathematical background for his interpretation of deviations from Ohm’s law in weak electrolytes. It dealt with the solutions of the Mathieu equation of period 4 pi and certain related functions and was beyond the comprehension of the chemistry and physics faculty. Only when some members of the mathematics department, including the chairman, insisted that the work was good enough that they would grant the doctorate if the chemistry department would not, was he granted a Ph.D. in chemistry in 1935. Even before the dissertation was finished, he was appointed assistant professor in 1934, and promoted to associate professor in 1940. He quickly showed at Yale the same traits he had at JHU and Brown: he produced brilliant theoretical research, but was incapable of giving a lecture at a level that a student (even a graduate student) could comprehend. He was also unable to direct the research of graduate students, except for the occasional outstanding one. During the late 1930s, Onsager researched the dipole theory of dielectrics, making improvements for another topic that had been studied by Peter Debye. However, when he submitted his paper to a journal that Debye edited in 1936, it was rejected. Debye would not accept Onsager's ideas until after World War II. During the 1940s, Onsager studied the statistical-mechanical theory of phase transitions in solids, deriving a mathematically elegant theory which was enthusiastically received. In what is widely considered a tour de force of mathematical physics, he obtained the exact solution