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This is a book guaranteed to delight the reader. It not only depicts the state of mathematics at the end of the century, but is also full of remarkable insights into its future development as we enter a new millennium. True to its title, the book extends beyond the spectrum of mathematics to include contributions from other related sciences. You will enjoy reading the many stimulating contributions and gain insights into the astounding progress of mathematics and the perspectives for its future. One of the editors, B. Engquist, is a world-renowned researcher in computational science and engineering. The second editor, W. Schmid, is a distinguished mathematician at Harvard University. Likewise the authors are all foremost mathematicians and scientists, and their biographies and photographs appear at the end of the book. Unique in both form and content, this is a "must-read" for every mathematician and scientist and, in particular, for graduate students still choosing their speciality.