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Building a bridge between mathematicians and industry is both a chal- lenging task and a valuable goal for the Institute for Mathematics and its Applications (IMA). The rationale for the existence of the IMA is to en- courage interaction between mathematicians and scientists who use math- ematics. Some of this interaction should evolve around industrial problems which mathematicians may be able to solve in "real time." Both Industry and Mathematics benefit: Industry, by increase of mathematical knowledge and ideas brought to bear upon their concerns, and Mathematics, through the infusion of exciting new problems. In the past ten months I have visited numerous industries and national laboratories, and met with several hundred scientists to discuss mathe- matical questions which arise in specific industrial problems. Many of the problems have special features which existing mathematical theories do not encompass; such problems may open new directions for research. However, I have encountered a substantial number of problems to which mathemati- cians should be able to contribute by providing either rigorous proofs or formal arguments. The majority of scientists with whom I met were engineers, physicists, chemists, applied mathematicians and computer scientists. I have found them eager to share their problems with the mathematical community. Often their only recourse with a problem is to "put it on the computer." However, further insight could be gained by mathematical analysis.