To analyze Brownian motion and the stock market and mosquito all at once, with the mathematics of the random walk, is to follow Poincaré’s slogan and give the same name to different things. Poincaré formulated his famous advice in his 1908 address to the International Congress of Mathematicians in Rome. He spoke movingly of the way doing complex computations can feel like “blind groping,” until that moment when you encounter something more: a common mathematical understructure shared by two separate problems, illuminating each in the light of the other. “[In] a word,” Poincaré says, “it has
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