This volume contains the proceedings of the conference ""Casimir Force, Casimir Operators and the Riemann Hypothesis - Mathematics for Innovation in Industry and Science"" held in November 2009 in Fukuoka (Japan). The conference focused on the following topics: Casimir operators in harmonic analysis and representation theory Number theory, in particular zeta functions and cryptography Casimir force in physics and its relation with nano-science Mathematical biology Importance of mathematics for innovation in industry