Berlin
The world's leading research university, until it wasn't.
Kernel
Wilhelm von Humboldt's reform of the Prussian university in 1810 invented the modern research university — teaching and research united, professors expected to publish. For a century afterward Berlin and Göttingen were where physics, chemistry, mathematics, and medicine actually advanced. The 1900–1933 generation (Planck, Einstein, Born, Hilbert, Noether, Haber, Heisenberg in his Göttingen years) is the last great central-European intellectual moment before the catastrophe.
What it gave the world
The modern research university (the Humboldtian model copied by Johns Hopkins in 1876 and from there across the United States). Modern physics — quantum mechanics, general relativity, the foundations of quantum chemistry. Modern abstract mathematics (Hilbert, Noether). Industrial chemistry (BASF, Bayer). The dye-and-pharmaceutical industries that defined the late-19th-century chemical economy.
Why it declined
1933. The Nazi expulsion of Jewish and politically dissident scientists was the single greatest brain-drain event in human history; within a decade the German physics tradition was operating in Princeton, Los Alamos, Cambridge, and Tel Aviv rather than in Berlin or Göttingen. The Manhattan Project is in large measure what happened when central European physics emigrated. By 1945 the center of physics was American.