in mathematics and the physical sciences, such as under the guidance of mathematician David Hilbert and the physicist Arnold Sommerfeld. At Göttingen Jordan became an assistant to the mathematician Richard Courant for a time, and then he studied physics under Max Born and heredity under geneticist and race scientist Alfred Kühn for his doctorate. Scientific work Together with Max Born and Werner Heisenberg, Jordan was a coauthor of an important series of papers on quantum mechanics. He went on to pioneer early quantum field theory before largely switching his focus to cosmology before World War II. Jordan devised a type of nonassociative algebras, now named Jordan algebras, in an attempt to create an algebra of observables for quantum mechanics and quantum field theory. While the algebras proved not to be useful for that purpose, they have since found numerous applications within mathematics. Jordan algebras have been applied in projective geometry, number theory, complex analysis, optimization, and many other fields of pure and applied mathematics. In 1966, Jordan published his 182-page work Die Expansion der Erde. Folgerungen aus der Diracschen Gravitationshypothese (The expansion of the Earth. Conclusions from the Dirac gravitation hypothesis) in which he developed his theory that, according to Paul Dirac's hypothesis of a steady weakening of gravitation throughout the history of the universe, the Earth may have swollen to its current size, from an initial ball of a diameter of only about . This theory could explain why the ductile lower sima layer of the Earth's crust is of a comparatively uniform thickness, while the brittle upper sial layer of the Earth's crust had broken apart into the main continental plates. The continents having to adapt to the ever flatter surface of the growing ball, the mountain ranges on the Earth's surface would, in the course of that, have come into being as constricted folds. Despite the energy Jordan invested in the expanding Earth theory, his geological work was never taken seriously by either physicists or geologists. Political activities Germany's defeat in the First World War and the Treaty of Versailles had a profound effect on Jordan's political beliefs. While many of his colleagues believed the Treaty to be unjust, Jordan went much further and became increasingly nationalistic and right-wing. He wrote numerous articles in the late 1920s that propounded an aggressive and bellicose stance. He was an anti-communist and was particularly concerned about the Russian Revolution and