Applications are plentiful. The first usage happened in optical interferometry, starting with the research by A. A. Michelson. Later, magnetic resonance, in particular NMR profited enormously from applications of the Fourier transformation. Imaging procedures, using x-rays or magnetic resonance for visualizing molecular structures and the interior of macroscopic objects are today among the most prominent applications of the Fourier transformation. Undoubtedly, clinical imaging in human medicine has profited most significantly from this simple mathematical transformation. A survey on these exciting consequences of the ideas of a great mathematician, who acted at the same time as a politician, is presented.