"Not only the physical but also the intellectual landscape of German-language mathematics in the early 1930s would be impossible to imagine without Gernan-Jewish mathematicians. Indeed, some fields of mathematics were completely transformed by their contributions. Number theory was transformed by Hermann Minkowski and Edmund Landau, algebra by Ernst Steinitz and Emmy Noether, set theory and general topology by Felix Hausdorff, Abraham Fraenkel and several others—to mention but a few examples. In many rapidly expanding fields of modern mathematics, German-Jewish mathematicians contributed ground-breaking research—such as Adolf Hurwitz in function theory, Max Dehn in geometrical topology, or Paul Bernays in the foundation of mathematics. However, German-Jewish mathematicians did not limit their interest to 'pure mathematics.' Carl Gustav Jacobi made major contributions to the theory of elliptical functions ( a field already shaped by many other Jewish mathematicians in the 19th century: Ferdinand Gotthold Eisenstein, Leopold Kronecker, Leo Königsberger etc.) as well as to mechanics. Karl Schwarzschild's dissertation dealt with celestial mechanics, which later became of mathematical interest for Aurel Wintner. As an astronomer well-versed in mathematics, Schwarzschild also turned some attention to Einstein's relativity theory; similarly Emmy Noether and Jacob Grommer also contributed to the mathematical basis for Einstein's theory. Arthur Schoenflies and others brought the group-theoretical classification of crystal structures to a new level. Richard Courant and the young John von Neumann worked on new ways of presenting the methods of mathematical physics and, specifically, quantum theory. Applied mathematics, an expanding field of German institutions in the 1920s, owed much to the work of Richard von Mises, and the mathematical engineering sciences of hydrodynamics and aerodynamics to the contributions of Theodore von Kármán and Leon Lichtenstein."