Paris
The capital of state-rationalist science.
Kernel
Where London is a financial city with science attached, Paris is a scientific city with finance attached. The École Polytechnique (1794), the École Normale (1794), the metric system (1795), the Académie des Sciences (1666 → modern form), and the Napoleonic Code (1804) make Paris the operational model of state-rationalist civilization. Lavoisier, Laplace, Lagrange, Fourier, Cauchy, Poincaré, Pasteur, Marie Curie — Paris is the city that produced most of the working mathematics of the 19th century.
What it gave the world
Modern chemistry (Lavoisier). The metric system and the gram-second-meter physical world. Statistical mechanics (Laplace, Fourier). Microbiology (Pasteur). The Curies. The Eiffel Tower as engineering manifesto. The Academy of Sciences model that every later national academy copied. Modern urbanism (Haussmann's Paris, 1850s–60s).
Why it declined (as research center)
World War I killed a generation of École graduates. World War II's occupation broke institutional continuity. Postwar physics centralized at U.S. universities and the European theory traditions migrated to Cambridge, Göttingen-in-exile, and (in CERN) to Geneva. Paris stayed culturally dominant; it stopped being where the working physics was done.