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...