Role and Importance of Mathematics in Innovation

This book collects the papers presented at the Kyushu University in Fukuoka in October 2015. On this occasion, the unifying theme was "The role and importance of mathematics in innovation". Innovation is in fact the cornerstone of creativity in all human endeavors. It involves "seeing" things from an entirely new, sometimes quite elementary, perspective. Innovation in mathematics is the bread and butter of mathematical creativity. Equally important is the innovation in the performance of mathematics which can be disarmingly simple but have profound consequences. The book illustrates two different key roles that mathematics plays in supporting innovation in science, technology, and daily life, namely, needs-based and idea-based. For the former, mathematics assists with sorting through the possibilities and putting matters on a more rigorous foundation and for the latter, mathematical models of the possible implementations play a key role. The contents of this volume report on productive and successful interaction between industry and mathematicians, as well as on the cross-fertilization and collaboration that occurred. The book contains excellent examples of the roles of mathematics in innovation and, thereby, the importance and relevance of the concept "Mathematics for Industry".