In 1922, Sommerfeld decided to spend a year the University of Wisconsin as a visiting professor, so Heisenberg took the opportunity to transfer to Göttingen to work with Max Born, succeeding Pauli as his assistant. With Born, Heisenberg constructed mathematical methods that furthered knowledge of the relationships of the periodic table. However, he again provoked the disagreement of Bohr and now Pauli, who had relocated to Copenhagen. Meanwhile, Heisenberg completed work for a dissertation on the less controversial topic of hydrodynamics. In particular, he focused on solving convoluted equations for the stability and turbulence of flowing fluids. Though Heisenberg's answers were incomplete, his dissertation was passed on the grounds that his handling was evidence of strong ability, and moreover because the subject had been an unusually difficult one for a student to tackle. Heisenberg encountered much less sympathy at his oral examination, however. The
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