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Industrial mathematics has become a fashionable subject in the last three decades. Today, there are many university groups and even research institutes dedicated to industrial and applied mathematics worldwide, proving that mathematics has indeed become a key technology. In this paper we first give a short account of the history of industrial mathematics. Using experiences from the Fraunhofer Institute for Industrial Mathematics (ITWM), we try to characterize the specific problem driven work of industrial mathematicians and take a look at future challenges.