PERSON
Joseph Fourier
The French mathematician who proved that any complex signal—a vibrating string, the flow of heat, the noise of a city—can be decomposed into a sum of simple oscillations, and whose insight about the interchangeability of the temporal and the spectral has become the mathematical skeleton of every signal-processing technology from radio to neural networks.
In 1807, Joseph Fourier submitted to the French Academy of Sciences a paper on the propagation of heat that the referees found so strange they declined to publish it for fifteen years: Fourier claimed that any arbitrary function could be represented as an infinite sum of sines and cosines. The claim seemed to violate everything the referees believed about the relationship between simple and complex—between the smooth periodicity of a trigonometric function and the jagged, discontinuous, utterly unlike character of, say, the temperature profile along a metal rod. The referees were wrong, and the paper, eventually published in 1822 as Théorie analytique de la chaleur, became one of the most consequential in the history of mathematics. The insight it contained—that the domain of time and the domain of frequency are dual representations of the same reality, that any signal can be
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